(The group of valued points of) a reductive group ver $p$-adic field is
called p-adic reductive group. Motivated by the Langlands correspondence,
representations of $p$-adic reductive groups over the field of complex
numbers are studied for a long time. Recently, motivated by the $p$-adic
or mod $p$ Langlands correspondence, representations over a filed of
characteristic $p$ is studied. I will talk about a recent development of
this theory.