In what sense? Thematically or by particular discipline? Thematically, areas such as 18th to early 19th century Irish history are barely touched compared to mid to late 19th century and forward. The American Civil War is painfully oversaturated, and basically a dying field. Either way, thematically you're going to find areas of neglect and areas of oversaturation in every region or time period. In my experience, the areas of neglect tend to be precursor periods that in many ways led to major events. Obviously these "major events" get the most attention because its exciting. But it leaves a lot misunderstood about the reasons leading up these events, or why they're even significant.
Disciplinarily speaking, we're technically still in the "cultural turn," which is still lackluster compared to military or political history. A lot of cultural and social history is still playing catch up, and inevitably mixing with their predecessors. On the other hand, to be more specific, histories focusing on space flight, science by and large, or transnational histories are still relatively rare. Check out your library next time.
Although I have to admit, your question is somewhat vague. Hopefully I've conveyed some kind of answer. I'm on my phone, so my patience for the tiny keyboard is dwindling.
It's not strictly history but there's an enormous amount of philological work that needs to be done in Arabic. We're literally still relying on the original work that was done in the 19th century by guys like Edward William Lane and Carl Caspari (as translated by William Wright). The most relevant recent updates to this kind of work was in mid-century Germany, for instance by Hans Wehr (only for modern Arabic) and Wolfdietrich Fischer.
We don't have a classical Arabic dictionary better than Lane. We don't have any etymological dictionary of Arabic. Not only do we not have a critical academic edition of the Qur'an, we don't even have the kind of base-level corpora and databases that would be necessary to start that kind of work. The Corpus Coranicum project will go some of the way towards compiling that material but the project won't be completed for at least another decade. Nor am I familiar enough the project to say whether or not it will actually end up being the kind of manuscript database that the field needs.
So yeah, if anyone wants to go out there and learn the half-dozen or so semitic languages that would be necessary to start work on these dictionaries and grammars, or slog through decades of painstaking work collecting, uploading, digitizing, hypertextualizing, etc. these corpora, I, for one, would be grateful!
Not a historian (only have a bachelor in History) but what I find frustrating is the oversaturation of the coverage on the Vietnam War and little else on Vietnamese history. As a Vietnamese-American I was educated in mostly European and Western history and every time I try to look into something about Vietnamese history it inevitably ends up being about the War. What I'm really interested in is the social and religious history of Vietnam during the Medieval or earlier periods. The most I get when I go digging is "Vietnam was occupied by China for the longest time, so culturally they are similar to the Chinese." Very frustrating to say the least.
From what I know, the field of history of Asia is a mess and really need a serious reform.
Not only are there many shortcomings in the knowledge base, there are also serious issues in interpretation. As an example, a recent thread asked about "China's relationship with its own history." Another asked "why Indian history is so under-represented." Feel free to read through the excellent replies of /u/desoulis and /u/keyilan in those threads.
To borrow the terminology used by the historian Antonio Andrade, there is a revisionist school and there is a newer counter-revisionist school. Good revisionists re-examine sources and interpretation and strive against euro-centrism. This is important because as we know that yes, there is a lot of euro-centrism in history.
Bad revisionists argue along the lines that "Asia was soooo much more advanced back in the golden days," that "Asian powers and Europeans were on parity when the two sides collided in the age of European exploration," and so on. When it comes to East Asian history, unsurprisingly they tend to rally around the mythology of Zheng He's voyages, and more recently around the discourse on Chinese firearms technology in the 16th-17th centuries. Further, a huge underlying belief is the "imperial" view of China, that it had continuity, unity, and control.
For examples from this sub, see 1, 2, 3.
For a good perspective, I like 4 and 5.
The "counter-revisionist" school views primary sources and interpretations much more critically. The reality is that both sides can and do agree on some key points, but to get there we have to ask critical questions.
As far as over-saturated fields go, I think any sub-field that has attracted a non-trivial number of rivet-counters is over-saturated.
Edit: format, added more links.
Speaking very broadly, the precolonial history (prehistory?) of Africa is understudied.
There are certain exceptions to that statement. Pharonic Egypt has captured the public imagination, and there are lots of scholars studying it. Ditto, the legend of Mansa Musa's hajj draws the imagination to the Mali empire, and archaeological and oral history is well represented.
But, other regions aren't so lucky. Pierre de Maret seems to be the only specialist on the societies of the Congo rainforest, since Jan Vansina retired.
I don't know of any work being done on the Ovimbundu States in what is now central Angola.
The kingdoms of the central sudan, Wadai and Dar Fur, don't turn up much recent research.
I suspect that part of the problem is political instability in DRC or Sudan makes planning archaeological digs or archival visits daunting.
Partly too, the problem has to do with academic resources and how they are allocated. Western universities trend to have financial backing and access to academic journal publishing that African universities and africa-based academics often lack. So, research tends to go in directions that reflect the interest of Western scholars, and doesn't necessarily represent African interests.
The American Civil War is a bit of an odd duck; I think most aspects of it have been very well explored individually, but I don't know of a work that's really integrated every aspect of it into a single, coherent picture.
Gary W. Gallagher remarked that there's a sharp divide between academic and public interest on the topic. The public wants to know all about the bloody battles, whereas the academics are often trying to talk about anything but the battles. The thing is, in any modern state fighting a war, the battles and the social/cultural/economic developments historians of the modern form love are deeply and closely intertwined.
To a historian of, say, gender relations in the Old South, it matters which road and which divisions Stonewall Jackson takes through the Wilderness, because the course of the war affects everything in an age of mass politics. The war did not end because of some grand aggregates, the war ends because U.S. Grant's army gets across the James River before Lee catches wind and lays siege to Petersburg. When Lee's army is no longer in the field, that's when the war's over, and there's nothing less certain than a clash of arms.
People like learning about battles, because there's contingency there. The events matter. The individuals matter. Mr. John Doe doesn't matter in a substantive sense in 'The evolution of the American family 1850-1900', because there are twenty million John Does precisely as important as him, which is not at all individually. The thing is, there's contingency everywhere, but many historians have a habit of reading history backwards; they see what happened, then look back to find out why. The problem is, that's not at all how people experience their lives. We look backwards, they live forwards. Edward Ayers feels very strongly about this; he assembled a digital history project in the early years of the internet, called Valley of the Shadow. It's a collection of primary sources related to two communities in the same valley -same soil, same peoples, same religion, etc- on opposite sides of the Mason Dixon line. Taking their perspective, nothing is foreordained. The people of the southern county voted against secession time after time, until events forced their hand. No one could have imagined that this community would be at the center of the greatest war in American history.
Looking backwards, we know the Union won and the Confederacy lost, so we tend to think of things prior to 1865 in terms of causing that outcome. But when the people we studied lived their lives, they didn't see it that way. When the shells fell on Fort Sumter in 1861, Lee did not shoot Grant an email asking if he'd like to meet in Appomattox Court House on April 9th 1865, because that's the only way the history books have the next four years going down. Both of them saw a wide range of possibilities ahead of them, not this single thread of inexorable logical progression the textbook narrative of cause and effect presents. Some people go so far as to claim the outcome of the war was inevitable from the outset, or even before the outset, which I just can't sign off on. Even if it was true, it cleaves a yawning chasm between the historian and the people they're charged with studying.
In 1861, nobody could have imagined that the Union would win a battle in Maryland in the second year of the largest war in American history against the army of a slave republic on the cusp of recognition by the major foreign powers because a few privates found a copy of the enemy general's (the son of an American revolutionary! A career soldier in the U.S. Army! A Federalist Whig!) complete orders wrapped around a few cigars, and that this victory would be the basis for the largest property confiscation in American history and the immediate and violent end of the most powerful system of slavery in the modern world. But there are historians who consider Union victory and emancipation an inevitability as early as 1848; they might know the events and the metrics perfectly, but there's more to history than names, dates, and numbers. If you're trying to capture the experience of the people who lived back then, to a degree you have to forget that you know what happens, because they sure as hell didn't.
So the battles matter. They're not the only events that matter, because this war is being waged by whole societies, but they do. So it's important to understand why they shake out the way they do. Every 'why' has a 'what', and every 'what' has another 'why' underneath it. Why is Spotsylvania a stalemate? Because Emory Upton's attack breaks into the Confederate works. Why does his attack break in? Because in an age of inaccurate blackpowder weapons (dating back to the sixteenth century), troops armed with cold steel can carry a defended position as long as they don't. stop.
That last point is important, because a myth that rifled muskets made previous offensive tactics obsolete is carried forward in most of the consensus literature, and the idea does much to shape peoples' perception of the battles. In this view, rifled muskets increased the power of the defender (because they shoot farther, which means more casualties) to the point that it was impossible to annihilate an enemy army in a single battle, which demands a different strategy. They believe that outdated tactics and new technology combined to produce a far more lethal battlefield.
The problem is that it's just not true in the American context. A weapon is only as accurate as the man aiming it, and with minimal training, soldiers on both sides were unable to use the weapon to its full potential. While its theoretical maximum range was north of five hundred yards, almost all infantry combat took place at less than a hundred. Casualty rates in the American Civil War were often twenty to thirty percent, which sounds like a lot when people tell you it's a lot. But really, battle casualty rates seem to have held steady at that level since the days of the Roman empire. Earl J. Hess and Paddy Griffith have put forward work demonstrating that the rifle-musket's impact on the war was overstated, and furthermore explain the indecisiveness of Civil War battles and the rise of entrenchments without ascribing it to improved firepower.
To understand the Civil War, you do have to understand the battles both on their own terms and in the broader context. If American Civil War generals knew how and why the armies of Napoleon's campaigns fought the way they did, and sought to emulate them, then a historian of the war should know it too. A historian should know that Napoleon and his generals directed sharp, decisive battles with large staffs of trained officers, with large armies of experienced soldiers divided into many specialized arms, and should see where the Napoleonic and American experiences differed outside the technology in play. They should understand how contemporary armies were fighting in Italy, the Crimea, in Austria and France.
It's not strictly history, but history of philosophy - very generally speaking, anything after Aristotle (300 BC) and before Descartes (17th century!) is quite looked over. In many cases non-western history of philosophy is barely even taught at undergraduate level.
This is a question, would American Indians/Native Americans be considered under-developed history? Maybe that requires more archeology? I know there was a tribe on the Gulf Coast that one missionary wrote about, but they died out before the next group of missionaries arrived.
What about South American Pre-Columbian Cultures?
I'm not a mouthpiece or anything, but food history, gastronomy, and the development and spread of food tends to be an ignored history among serious historians.
Most of the time people's interest only goes as far as the Columbian exchange of new and old world crops, Pre-history diets, and medieval/Renaissance cuisine from SCA groups. Which is very unfortunate, since I find food history to be very interesting in its own right, it's food after all, we've been eating cooked food since the invention of fire yet we can't seem to remember what we ate only a hundred years ago.
When researching my bachelor thesis on reactions to nomadic warfare on the Balkan and in Russia, I noticed two fields which are quite underresearched.
Hungarian military history, especially that of the hussars, which I was very interested in, has a severe lack of English secondary sources. Most influential books (basing this purely on citations in the English works, as I have no better way to view it) are in Hungarian, which isn't a very usual language in international academic discourse.
Another field is that of small war. Many military historians reference the lack of literature on small war, the part of warfare that consists of raiding, reconnaissance, et cetera, before the Napoleonic era (and perhaps also after). The issue is that the few historians who do write on it seem to be stuck doing two things:
Defining small war, partisan, guerilla, parties, and so on.
Showing that small war was definitely relevant and common before Clausewitz theorized on it.
The issue is they rarely go into explaining how small war worked, why it worked, what kind of troops were effective and why; essentially any question that moves from the descriptive. It is a field in its infancy, as far as I can tell.
As someone who had training in science and then took some classes in History at a University level in general the scientific literature of history is absolutely horrible. From my experience history journals accept much lower quality of papers than scientific journals and is one area which I think history is really underdeveloped. On the flip side, historic books/textbook are often much better written than scientific books/textbooks.