So many aspects of Byzantine history have been reevaluated in the last few decades, its tough to answer this question concisely, but I'll give it a try.

The traditional view of the Byzantine Empire was heavily coloured by Western European historians who treated it as an 'other'. Even calling it the Byzantine Empire fits into that: historically the Byzantines always referred to themselves as the Roman Empire, or Romania. It was only named 'the Byzantine Empire' by a 16th century German historian.

Other historians, including Gibbon, often presented the Byzantine Empire as a realm of medieval superstition and absolutism, in contrast to their own Age of Reason and Enlightenment. In this view, the Byzantine Emperor was God's representative on Earth, and to disobey him was to risk damnation. This religion dominated view of Byzantine society was reinforced by the traditional view of the Iconoclasm controversy, which looked to Western European historians like the distillation of everything they were trying to escape from in their own societies and their recent history (Church censorship, the 30 Years War etc.). Finally, to most early Byzantine historians, the Empire suffered greatly from comparisons from the earlier Roman state, with its (perceived) rigorous discipline and manly virtues. The contrast with the effete, scheming Greeks who never did their own fighting (an image partially taken from Western European Crusading narratives) is clear.

So that's the traditional view, now on to how that has changed. I think the two main trends in changing the traditional views have been more modern methods of source criticism, and more objective scholarship that is willing to challenge the old views.

An example of both of these trends is The Byzantine Republic by Anthony Kaldellis. I can't recommend this book highly enough if you're interested in learning more about this topic. Its thesis is that Byzantine society, far from being a God-ordained absolutist state, actually inherited a fair bit of republicanism from Rome. I think Kaldellis takes the point a bit too far, but one of his basic themes makes a lot of sense: if the Emperor was God's regent on Earth, why were there so many coups, rebellions, plots and riots? His answer is that the whole God/Emperor thing comes almost entirely from propaganda issued by the Emperors or from works they commissioned. Taking those works at face value, as past historians have done, means that we are only seeing the Byzantine state as its leaders wanted us to see it. It would be a bit like judging the political situation in Russia purely by reading Kremlin press releases, to put it mildly, you are not getting the whole truth.

In terms of reevaluations of the religious aspects of Byzantium, including issues like the Monophysite 'heresy' and Iconclasm, I know there has been a great deal of work done challenging how deep these divisions went, how long they lasted, and in general how important they were, unfortunately I don't feel competent to address them.

Hope this helps!