So let me say off the bat that "Holocaust Studies" is a generalized term; as generalized as WWII Historian, World Historian, ect. ect. I'm guessing I was paged for this reason specifically because it seems out of place since I have acquired this flair around two years ago. Lets just call it "Holocaust History" in this context.
Now this category can grapple a large amount of different things; again large generalization. Subjects pertaining to this can be:
Answering the Jewish Question, How did the Final Solution come about?
That is the debates still are: Functional vs Intentional to solve the Jewish Question. Now I myself subscribe to functionalism, and It would be safe to say that most current works and historians lean towards this idea, as it is reoccurring theme supported by a mountain of evidence.
This is to say that the Holocaust was the product of a functional means of dealing with undesirables. This being the eventual lead up to industrialized murder rather than an intentional goal of genocide. I have tried to find the post made by /u/commiespaceinvader when they had answered a question posed on why Germany did not export undesirables. Well in the case of that question the answer was that they had tried multiple times, Haavara Agreement with Palestine, Madagascar, ect. Being functionary started off small. Voluntary Aryanization: acquisition of Jewish property, businesses. The creation of camps for political, anti-christian, emigrants, Jews ect. ( Dachau, Sachsenhausen, Buchenwald, Lichtenburg; with more camps following the annexation of Austria with the creation of Mauthausen, Ravensbruck. ect. ect. The plan of exportation as mentioned above, with further theft of Jewish property (the buy back of their own property after leaving Germany) to gauliters taking it upon themselves and murdering their Jewish populations, to the end product of industrialized genocide and the creation of camps as Auschwitz - Birkenau, Sobibor, Treblinka ect.
Great book if you're interested is
Other Subjects that one could pursue in "Holocaust History" are:
Eugenics movement that operated within the Holocaust and after, with sub subjects such as the Kaiser Wilhelm Institute, Dr. Alfred Höche and Dr. Karl Binding and the Racial Hygiene movement. The eugenics movements within the United States and Canada. Weird outliers such as Dr. Mengele I posted a great deal of information of the Human experimentation done by Dr. Mengele. HERE
Great reads that I have found on these subjects include:
Muller-Hill, Benno "Human Genetics and the Mass Murder of Jews, Gypsies, and Others." In The Holocaust and History: The Known, the Unknown, the Disputed, and the Reexamined, edited by Michael Berebaum and Abraham J. Peck Indianapolis: Indianapolis University Press, 1998.
Lifton, Robert Jay. Medical Killing and the Psychology of Genocide: The Nazi Doctors. Newyork: Basic Books, 1986
Nyiszli, Miklos and Richard Seaver and Tibre Kremer. Auschwitz: A Doctor's Eyewitness Account. Newyork: Arcade Publishing, 1960.
Weiss, Shila. The Nazi Symbiosis: Human Genetics and Politics in the Third Reich. Chicago: Chicago University Press, 2010.
Other debates and challenges are the growing problem of Holocaust Revisionism, Holocaust Denial, plague of David Irving ect. There will always be those who are ignorant, racially intolerant that will always fuel historians to pursue further refinement and collection of evidence in these "plateaued" subjects.
Personally I still want to do research into Sonderaktion 1005, and "The Farmers", im trying to find another post from a flaired user on "The Farmers" just such an interesting subject.
In closing, i'm not going to lie. I wish I had time like /u/commiespaceinvader, few of his posts have newer books ive still not gotten to. I hope in this post I have given some insight into the mountain that is Holocaust History "Holocaust Studies" (semantics arguments are silly), There are so many avenues, I don't think this post can even justify the extent of a question like this. Ive added some books that I found excellent for the areas I mentioned in terms of providing a Historiography of sources I have encountered. Thank you /u/AnnalsPornographie it was nice to sit down for an hour and open some book boxes and note books.
Raul Hilberg is considered the founder of Holocaust history, and I'm pretty confident other aspects of Holocaust studies also emerged out of his work. He published The Destruction of the European Jews in 1961. He is also responsible for one of the enduring frameworks we use when we discuss the Holocaust, the tripartite division of people involved into Perpetrators/Victims/Bystanders. (This has been further developed and modified following his introduction of the concept, but it remains foundational to the field.) Building on the answer of /u/stormraughtz, (and a big shout-out to you for jumping in to tackle the question, which indeed covers a huge and diverse field of study!): while the intentionalist vs. functionalist debates and the issue of Holocaust Denial have not been entirely resolved or gone away, I would say that the most prominent contemporary issues in the field are the following:
What role did non-German collaborators play in the Holocaust, particularly in eastern europe? This question has risen in popularity since the publication of the english-language version of Jan Gross' book Neighbors in 2001, which talks about rural Poles in the village of Jebwadne murdering their Jewish neighbours in a massacre in summer 1941.
How does thinking about the German expansion during WWII as an empire, and occupied territories in the east as "colonies" help us to understand what happened? This draws on existing theories of Colonialism, and has been employed by Mark Mazower Hitler's Empire and Wendy Lower Nazi Empire Building and the Holocaust in Ukraine. Historians debate how far we can explain the Holocaust using theories from colonialism, but most agree it is one potentially valuable tool in the historical toolbox.
Incorporating new territories in eastern and south-eastern Europe into the history of the Holocaust. The specifics of the Holocaust on Russian soil (that is, even further east than Ukraine, Belarus, etc), the experiences of Jews in Transnistria, the region in the south-western USSR that was occupied and administered by Romania rather than the Germans, and the Holocaust in the Balkans (particularly Yugoslavia) are all receiving increased attention right now. I know of two books that will come out this year on these places, by Kiril Fefferman and Diana Dmitru. This shift in focus reflects the opening up of previously-unavailable Soviet archives, as well as a new generation of historians who know more eastern languages AND are interested in studying the Holocaust.
Other things that have gained more attention from Holocaust historians over time: gender history, and the role gender played in the Holocaust; studies of sexual violence; the use of oral history interviews and memory sources (created decades after the events) as primary sources.
The focus here remains firmly on Holocaust history. I would say that the development of other branches of Holocaust studies (studies that look at some aspect of the Holocaust in relation to literature, film, theatre, music, religion) have also been on the rise recently, i.e. post-2000.