Today, the popular perception of Al-Andalus is that of a tolerant centre of arts and learning. But I can't imagine that this is what 15th century Spanish academics and public alike would have viewed the Moors. How has perceptions of Al-Andalus evolved? Furthermore, what's the current academic discourse among historians regarding Al-Andalus?
Quick point first up - "Moors" is an outdated term and while you might occasionally find it in use, it isn't really a preferred term. "Andalusi" is a more accepted term these days.
Study of al-Andalus, and views and approaches towards that period have changed significantly over the centuries. This question is something that people write entire papers over!
I think, in essence, the past 1-200 years has seen a revival in interest in al-Andalus in the region. For centuries post-Conquista of course it was an era that was heavily demonised and tied up in Spanish religious fervour. Maria Rubiera Mata and Mikel de Epalza in what I think was a pretty good paper on the topic of the revival of interest in al-Andalus described it as "locking the tomb of the Cid", where conservatives and other right-wing academics argued heavily against revising the then-common Iberian view of al-Andalus. Their view was essentially that al-Andalus was not really a part of Iberian history, that it was rather a part of middle eastern and specifically arab history and was to be rejected as something foreign to Spain. Study of al-Andalus wasn't Spanish history, it was the history of Arabs who happened to be IN Spain but weren't really part of, or relevant, to Spain.
It took a pretty long time, but that view eventually faded. Nowadays there is of course a consensus among scholars that al-Andalus is - unsurprisingly - an important part of Iberian history. I think the popular perception of al-Andalus as that of a tolerant centre of arts and learning as you describe isn't that far from how many historians see it, although of course in scholarship that perception is always qualified with a lot of research that's been done into exactly what "tolerant" means in the context of a middle ages european society - which is to say, they were tolerant for their time. A lot of research seems to indicate that while Christians and Jews, especially the latter, received a lot of privileges in al-Andalus that muslims and jews would not receive elsewhere in most other regions of europe, they still weren't necessarily equal politically.
As for current discourse - I assume you're asking here about what are the big, active areas of research. Well, there's a lot of important archaeological work ongoing. There's been a lot of interesting stuff in the past few decades about irrigation in particular, I'd say. Jose Roldan-Canas (missing some diacritics there since I've got an english keyboard, sorry) has put out some excellent work relating to that topic, for instance. Hydraulic systems in al-Andalus as well as related areas such as pottery and agriculture is a really good area of activity at the moment. I'd say this is a 'big deal' area of research in the past few decades.
And it's contributed a lot to understanding of those fields in neighbouring regions as well as in the middle east too. Which brings me to the next big point of emphasis in research surrounding al-Andalus, where there's a lot of scholarship focusing on the influence of al-Andalus outside the Iberian peninsula. What are the areas of inquiry? Well, lots. Trade, poetry, pottery, and again, irrigation, and literature, I would say are the major ones, but there are of course many other lines of inquiry ongoing.
Here's that paper I cited before. You'll probably need database access to get a copy, though, unfortunately.