To me, one of the most interesting debates about history is the debate about whether "great men" cause history to happen or whether "structures" or "conditions" cause history to happen.
The "great men" theory (I put this in quotes because we would no longer accept the use of "men" since it excludes women) argues that, for example, WWII happened because of who Hitler was. His existence and his particular combination of talents and madness pushed Germany to start the war.
By contrast, the other view of history says that individuals are more or less irrelevant. It argues that WWII would have happened even if Hitler had been killed in WWI. It says that the circumstances facing Germany and the other European countries would have led to the outbreak of war.
This is a very important debate because it affects how we think about history and what we think about how we can use the lessons of history to give ourselves a better chance at making the future better than the past was.
I think that many debates are involved in "history." One particular debate, as previously suggested, is the idea of what to include and what to exclude. The process of inclusion and exclusion in the historical narrative causes a great deal of debate and challenge within the historical community. Underlying this is the presence of bias and personal slant. For example, the teaching of the Age of Exploration looks very different on the part of one who believes that the imperialism that resulted was a good thing as opposed to one who believes that it legitimized slavery and the oppression of societies. In America, for example, generations of students were taught that Columbus was a pioneer and the founder of America. It has only been in the last thirty or so years that this view has been tempered with the reality of his misdirection in navigation and the emergence of the "Columbian Exchange," where indigenous people gave advice, goods, and support to Columbus while he gave diseases and enslavement in return. The problem in both is for students to assess what they feel is "historically valid." I think that this is probably where challenge lies in the debate of history, in terms of being able to determine criteria that assesses validity and authenticity in the historical discourse.