What's the most popular modern APL?
Probably q simply due to its connection to kdb
not proprietary: NARS, ngn/k, J, klong, aplette, gnu apl, kona
javascript: ngn/apl, oK
calculator (free software): ivy
dead but the body's still warm (free software): xxl, nial,
dead but the body's still warm (proprietary): aplx, a+
There's a bunch missing here because everyone alive has written an APL interpreter at some point (Ken Thompson did for example but it's ancient history and has a few descendents), but listing all of them would take hours. Especially if we're getting into historical stuff.
They've been pretty heavily studied, though, certainly:
https://vector.org.uk (APL journal going back almost forty years)
If you have access to the old IBM journal, you'll find stuff that's past fifty, the first book on it is 58, and it itself is past sixty now.
I vaguely remember it was even packaged in Ubuntu multiverse and/or Debian at some point.
The "electric" GUI concept (The "+" in "A+" - without the GUI it was just called "A") was much simplified in k2 - it was fast, simple and extremely effective even though it didn't really look good - it is, in fact, the only environment I've ever had a chance to use where having a GUI is as simple or simpler than writing a batch program -- see e.g. 15-Puzzle[0] or the spring simulation[1] (even though the canonical example is the S- spreadsheet which you can find at the same site).
"Mostly dead" may be more accurate, I'll grant.