Why should a philosopher care about the nature of belief? Back in the 1980s and 1990s, when I was a student, there were two main animating reasons in the Anglophone philosophical community. Recently, though, the literature has changed.
One of the old-school reasons was to articulate the materialistic picture of the world. The late 1950s through the early 1990s -- roughly from Smart's "Sensations and Brain Processes" through Dennett's Consciousness Explained -- was (I now think) the golden age of materialism in the philosophy of mind, when the main alternatives and implications were being seriously explored by the philosophical community for the first time. We needed to know how belief fit into the materialist world-picture. How could a purely material being, a mere machine fundamentally constituted of tiny bits of physical stuff bumping against each other, have mental states about the world, with real representational or intentional content? The functionalism and evolutionary representationalism of Putnam, Armstrong, Dennett, Millikan, Fodor, and Dretske seemed to give an answer.
The other, related, motivating reason was the theory of reference in philosophy of language. How is it possible to believe that Superman is strong but that Clark Kent is not strong, if Superman really is Clark Kent (Frege's Puzzle)? And does the reference of a thought or utterance depend only on what was in the head (internalism) or could two molecule-for-molecule identical people have different thought contents simply because they're in different environments (externalism). Putnam's Twin Earth was amazingly central to the field. (In 2000, Joe Cruz and I sketched out a "map of the analytic philosopher's brain". Evidence seemed to suggest a major lobe dedicated entirely to Twin Earth, but only a small nodule for the meaning of life.)
These inquiries had two things in common: their grand metaphysical character -- defending materialism, discovering the fundamental nature of thought and language -- and their armchair methodology. Some of the contributors such as Fodor and Dennett were very empirically engaged in general, but when it came to their central claims about belief, they seemed to be mainly driven by thought experiments and a metaphysical world vision.
Literature on the nature of belief has been re-energized in the 2010s, I think, by issues less grand but more practical -- especially the issue of implicit bias, but more generally the question of how to think about cases of seeming mismatch between explicit thought or speech and spontaneous behavior. Tamar Gendler's treatment of (implicit) alief vs. (explicit) belief, especially, has spawned a whole subliterature of its own, which is intimately connected with the recent psychological literature on dual process theory or "thinking fast and slow". Does the person who says, in all attempted sincerity, "women are just as smart as men", but who (as anyone else could see) consistently treats women as stupid, believe what he's saying? Delusions present seemingly similar cases, such as the Cotard delusion which involves seemingly sincerely claiming that one is dead. What are we to make of that? There's a suddenly burgeoning philosophical subliterature on delusion, much of it responding to Lisa Bortolotti's recent APA prizewinning book on the topic.
By most standards, the issues are still grand and impractical and the approach armchairish -- this is philosophy after all! -- but I believe their metaphilosophical spirit is very different. What animates Gendler, Bortolotti, and the others, I think, is a hard look at particularly puzzling empirical issues, where it seems that a good philosophical theory of the nature of the phenomena might help clear things up, and then a pragmatic approach to evaluating the results. Given the empirical phenomena, are our interests best served by theorizing belief in this way, or are they better served by theorizing in this other way?
This is music to my ears, both metaphilosophically and regarding the positive theory of belief. Metaphilosophically, because it is exactly my own approach: I entered the literature on belief as a philosopher of science interested in puzzles in developmental psychology that I thought could be dissolved through application of a good theory of belief. And at level of the positive theory of belief, because my own theory of belief is designed exactly to shine as means of organizing our thoughts about such splintering (The Splintered Mind!), seemingly messed-up cases.