Abstract: The theory of complex representations of reductive p-adic groups, for instance GL(2,Q_{p}) where Q_{p} is the p-adic completion of Q, is an essential part of the Langlands program. Its links with number theory and geometry requires to study representations in vector spaces over fields different from the field of complex numbers, or even in modules over commutative rings, for instance over finite fields or over Z[1/p]. We will give an overview of the main problems in this area and of recent progress towards some of them.