Lusztig's theory of character sheaves for connected reductive groups is one of the most important developments in representation theory in the last few decades. In this talk, I will describe some basic algebro-geometric techniques underlying this theory and explain the need for a theory of character sheaves on jet schemes of reductive groups from the perspective of the Langlands program. Recently, R. Bezrukavnikov and I have developed the "generic" part of this desired theory. In the simplest nontrivial case, this resolves a conjecture of Lusztig and produces perverse sheaves on jet schemes compatible with parahoric Deligne--Lusztig induction.