So basically, history in the last 50 years has moved from the "Great Man History", or more specifically the standard politico-military histories that were oh so popular during the late 19th and early 20th centuries, towards cultural/social history.

The difference between cultural and social history is pretty goddamn slim, but basically they both study the history of people. An intermediate step was called Marxist history, or the study of the "proletariat", and that got cleaned up to (it got a haircut, put on a suit, and threw out its Che Guevara t-shirt. Fuckin' sellout.) "bottom up" history. Basically, all four really tried to figure out what everybody else was doing when the "Great Men" went out a'conquer-in.

In the case of Cultural/Social history, they really try to understand trends, experiences, and groups. Social historians look mainly for those trends and macro-level conclusions, which can be extrapolated down to fit smaller groups (usually). OTOH, cultural history focuses on "microhistories", or really small tales, vignettes, and stories of people, places, traditions, rituals, or other really unique things. These stories are then wrapped up into a larger connection to society in that place, at that time.

Actually, I would kinda say that Cultural history has really "taken over" history, and its really now the dominant, hegemonic, methodology for most historians. Or it is at my school, its hard to tell what the outside world is like sometimes. Schools are like echo-chambers in some ways.

A great person to read, to try and see this method in practice is Natalie Zemon Davis. She has a collection of Essays (Society and Culture in Early Modern France), which is 8 essays that detail specific groups, rituals, etc. of early modern French life, and then connect them to great French Culture, and also modern society. An example: She has one essay about Journeyman printers in Lyons. These printers formed a group, the Griffarions (I think I spelled that right), which was sort of a trade union. This "union" then went around the town pissing off all the Protestants, killing scabs, and raising hell. The protestants kicked them out following their rise to power in Lyons. That essay really shows what Cultural History is: I take a small topic, explore it in detail, then connect it to something larger and more meaningful.

The major problem I have with cultural history, and especially its stats in the discipline now (again, where Im at in it) is its too powerful. Before, there was no balance between the "great men" and the little guys. Now theres no balance the other way, and nobody wants to talk "traditional" European history. Thats great if you really love, say, sexual history, and writing about the sexual mores of Victorian women really gets your motor running. In this methodology, youll do well. Me, I like War. And Tanks. And Strategy. Im a "lines on the map" kind of guy. I really want to talk about Bismarck, and the Molktes, and Marshall. But thats not the history thats popular right now, so sometimes I feel left out of the whole "micro-cultural-history" party. So thats my big criticism with the current direction of things. That and the fucking post-modernist school. Seriously. Fuck those guys.

Also, I notice your flair is Japanese history. Im not up on my Asian historiography, but Im pretty sure that native Asian historians are likely practicing their own specific kinds of historiography. There is enough trouble trying to apply what Ive just said to other Anglophone countries like England, let alone the rest of Europe, or Asia.

what sort of epistemic theories underpin different "camps" in current historical practice?

I would answer this, if I knew what it meant.

In some ways the Great Man theory was a metanarrative, and I think metanarratives are in general less emphasized these days. The Great Man theory suggests that well... Great (or more perhaps "important") Men are the driving force in history. You acknowledge this in your question, but I think the question of "what makes history go" as you say has fallen a bit out of fashion. Certainly there are still people who are trying to answer that question, but many historians have eschewed it in favor of using different frameworks to explain different things.

As an example the Marxists metanarrative, which is quite far from the Great Man theory in that it posits that class conflict is the driving force behind history, has also pretty much gone out of fashion. But that does not mean that Marxist analysis has gone entirely out of fashion. Instead, it means that historians tend to use his insights about class and historical materialism in a more focused way. To poke and prod some bit of history to see what insights come, rather than try to place them into a grand narrative.

I can not really speak for everyone, so I will just speak for myself. To me historical methods and theories are part of a sort of "toolbox" from which I can take out a particular thing when it is the right tool for the job. I will say that this - as a rule - is a bit of a post-modern position. I don't really think of myself as primarily a post-modernist. However, I do think that is probably has some post-structuralist leanings as you'll notice when you read the rest. So be it.

For example, I think discourse analysis can be incredibly powerful and useful as an analytical tool. But at the same time I don't need to buy into the idea that "all the world's a text." Just as seeing the usefulness of post-modern theory in general to understand the way people understood (or understand) the world, how their world view and beliefs or "knowledge" influences their life and decision making does not mean I need to reject the notion of objective reality.

Gender theory has become very important for analysis as well. Joan Scott's article from 1986 sort of launched that. Even though a lot of work has been done since then, it still serves as a great introduction to the concept. It's available here: http://facultypages.morris.umn.edu/~deanej/UMM%20Home%20Page/2001/Readings/Gender/Scott_Useful%20Category.pdf

William Sewell has made a somewhat similar point in his 2005 book Logics of History in which he discussions social and cultural history both at length. He thinks that both social and cultural history have offered important breakthroughs but that dedicating yourself to only one or the other can be a bit too limiting.

I just remembered I answered a similar question to this a while back and dug up my answer. It is similar, but I included a list of relevant works by category in that one. If you want to see that, you can read it here: http://www.reddit.com/r/AskHistorians/comments/1pa59n/historians_of_all_fields_what_are_some_of_the/cd0m4fw