The first complete computation of higher algebraic K-groups was done by Quillen, who computed all the K-groups of finite fields.  In these cases, the finite fields all come equipped with an action by a cyclic Galois group G, and one can consider the equivariant algebraic K theory, a refinement of algebraic K-theory to a genuine G-spectrum. In this talk I will discuss some recent work on computing the equivariant algebraic K-groups of finite fields.  We are able to reduce the computation to the RO(G)-graded coefficient groups of certain equivariant Eilenberg MacLane spectra, giving a complete answer in all cases.  This talk is based on joint work with Chase Vogeli.