Harish-Chandra induction and restriction functors play a key role in the representation theory of reductive groups over finite and local fields. Constraining a trivial action by appropriate unipotent subgroups, which is part of their definition, results in simple combinatorial commutation relation between induction and restriction from and to Levi subgroups. This allows one to effectively construct and classify representations of such groups. In this talk I will describe generalisations of these functors that are suitable for profinite groups. This is a joint work with Tyrone Crisp and Ehud Meir.