Iwahori & Matsumoto (1965) studied Iwahori subgroups for Chevalley groups over p-adic fields, and Bruhat & Tits (1972) extended their work to more general groups.
Roughly speaking, an Iwahori subgroup of an algebraic group G(K), for a local field K with integers O and residue field k, is the inverse image in G(O) of a Borel subgroup of G(k).
More precisely, Iwahori and parahoric subgroups can be described using the theory of affine Tits buildings.
If G does not satisfy these hypotheses then similar definitions can be made, but with technical complications.
When G is an arbitrary reductive group, one uses the previous construction but instead takes the stabilizer in the subgroup of G consisting of elements whose image under any character of G is integral.