It seems rather strange to think of history as a dead subject, since there have been multiple revolutions in historical thinking since the 1950s.
To give the briefest overview of that, top down political history and diplomatic history was rejected in favor of a social history, which itself was divided into numerous different tendencies (Marxist inspired, cliometric, social science history more broadly, a history of mentalities, etc.), which themselves sometimes during the 80s and 90s were challenged by post-modernist and cultural historical accounts. That was, to put it lightly, a pretty big deal and had quite the effect on the methodology of historians.
To give some more concrete examples -- mostly from those turbulent 80s and 90s -- in French history, the Marxist interpretation of the French Revolution was dealt a fatal blow by François Furet, who rejected the importance of the French Revolution but also drew a powerful connection between the ideas of the French Revolution, the Terror, and Bolshevik Terror. Of course, this revisionist position (as it is called) is hardly unchallenged and historians more sympathetic to either Marx or to the Jacobins sometimes attempt to provide powerful counterarguments to the Furet.
Additionally, the dimension of gender and race in the French Revolution are becoming much more deeply studied, be that questions about how the Revolution influenced the lives of women or how the various colonies of France responded to the Revolution. Particular focus is given to Haiti and the Haitian Revolution is often imagined as the beginning of human rights. A rather impressive change from the tendency to never talk about the Haitian Revolution just two odd decades ago.
Moving from French history to German, the Sonderweg thesis was dealt a fatal by Geoff Eley and David Blackbourne in the 80s and while I can think of some older historians who still embrace it, the impression I have is that younger historians of Germany have completely rejected it as an explanatory account.
Similarly, the Historikerstreit happened. Roughly -- and hopefully without imputing too much of my bias here, because it is a notoriously complicated and contentious debate -- in Germany some historians were interested in historicizing Nazi Germany and putting it into comparison with Bolshevik Russia, while other historians argued that Nazi Germany (particularly in this discussion the Holocaust) were unique and not comparable (at least in the way that the pro-historicizers wanted them to be). Exactly who one this debate is complicated (read no one really did), but comparisons of Nazi Germany and Stalinist Russia have become an interesting historical discussion either in their rejection or in their acceptance thereof.
Most of those changes though are changes that happened a few decades ago (but from my perspective haven't really hit mass consciousness yet!), if you want more modern breakthroughs (or emerging fields):
The new history of capitalism -- After the financial crisis, a new generation of historians became interested in understanding the dynamics of capitalism and how capitalism evolved. A particular subinterest is the history of slavery and capitalism and whether the Williams thesis is true (was slavery necessary for capitalism).
The history of the carceral state -- While there has been some study of prisons (including by Foucault, obviously!), the issue of mass incarceration is finally getting a lot of airtime as it were within the historical discipline and a number of scholars are investing the history of imprisonment (and with that racism, political economy, etc.) in the United States.
New American Political History -- I am not sure if this will be the name of the field, but it is what I call it. Historians under William Novak (amongst others) have been rehabilitating political history by keeping the history concerned not just with high politics but with the impact of those politics on the lives of ordinary people.
Rehabilitation of the Austrio-Hungarian Empire -- There was already a rehabilitation of the Holy Roman Empire, but popular works are now arguing that rather than embracing a liberal nationalist narrative of Austria Hungary as being a prison of nations, we might instead view it as a, obviously flawed, multinational empire with its own dreams to national identity that was destroyed by both World War I but also by a nationalizing middle class.
The East in European History -- Say what you will about Tony Judt, but Postwar attempted to bring the East into greater focus rather than shunting it to the side of European History. I would say we can see similar things with Synder's Bloodlands, albeit Bloodlands has been greatly criticized (for good reason, I might add!). But even with those examples, there's been a shift to talking about the Holocaust by bullets in the East rather than just the Holocaust by gas chamber. Similarly Eastern Europe defined as a land between multiple empires -- Russian, Ottoman, Austro-Hungarian seems to be taking hold as well.
I think that's an unrepresentative list of where historians are breaking new and untapped ground. It is unrepresentative because I myself am a Europeanist with some Americanist sympathies, so anything happening outside of the Europeanist or Americanist world I am completely unaware of, so I could not at all help with say Indian history or Middle Eastern history or even the pre-early modern period in European history. I also have the impression, but might be mistaken on this front, that digital humanities and public history are becoming big things, but since I do not study either, I could provide no guidance on how they work.
Sources on much of this:
Historical revolutions -- Richard J. Evans In Defense of History, but ignore pretty much everything he says about postmodernism. Geoff Eley's The Future of Class in History and A Crooked Line.
French Revolution -- The French Revolution: Recent Debates and New Controversies an anthology edited by Gary Kates.
Sonderweg -- The Peculiarities of German History two works in one by David Blackbourne and Geoff Eley.
Historikerstreit -- Forever in the Shadow of Hitler a collection of texts with no introduction or editorializing because none of the authors who owned the rights to the text could come to any agreement. Compare Evan's In Hitler's Shadow which is his personal account.
Comparing the Soviet Union and Nazi Germany -- Beyond Totalitarianism: Stalinism and Nazism Compared, edited by Geyer and Fitzpatrick.
The New History of Capitalism -- Two good review articles are "Capitalism and Slavery" by John J. Clegg in Critical Historical Studies (albeit I find it a tad too dismissive of the challenges of postmodernism and of the importance of agency) and "Reassembling the Economic: New Departures in Historical Materialism" by Kenneth Lipartito in American Historical Review
History of the Carceral State -- A lot, but I do not think a decent survey has been written yet, so it is all too diffuse. I would say a good article to get started with would be Heather Ann Thompson's "Why Mass Incarceration Matters" in the Journal of American History. Gottschalk is also pretty influential here, albeit I would say she does not focus on race enough, but her book Caught is quite good. Khalil Muhammad's The Condemnation of Blackness: Race, Crime, and the Making of Modern America is great long term account of race and criminalization.
New American Political History -- The two central articles are William Novak's "The Myth of the “Weak” American State" and "Long Live the Myth of the Weak State? A Response to Adams, Gerstle, and Witt" both in American Historical Review. The second is part of a special issue dedicated to the concept, while the first is a review of the research. A good anthology on the topic The Democratic Experiment: New Directions in American Political History, edited by Jacobs, Novak, Zelizer.
East in European History -- Postwar and Bloodlands, but better books might be Ordinary Men by Christopher Browning, Neighbors by Jan Gross. Although those too might be a bit too national in character. A more transnational work would be Shatterzone of Empires edited by Bartov and Weitz. Bartov has also written a good critical review of Bloodlands.
Edit: By the by, the type of history that replaced political history is often called "new social history" and the postmodernist influenced history that displaced it is often called "new cultural history". That was not at all clear from my description. Sorry!