Student or Learner
"As I understand it, exceptions are possible, but I don't know under what/which conditions."
"What" sounds more natural to me, but I'm not sure if it's truly better than "which."
***neither a teacher nor a native-speaker***
"What" makes it an open set, while "which" makes it a closed one.
what conditions: Any condition, no number can be given.
which conditons: aforementioned conditions, of limited number.