Let G be a finite group.  We can consider G-equivariant cohomology theories on G-spaces, which are given by G-equivariant spectra.  These spectra don't just have homotopy groups, but rather homotopy "Mackey functors," and this extra structure has proved useful in calculations.  If our spectrum has a G-ring structure, then recent work of Strickland and Brun shows that its zeroth homotopy groups form a "Tambara functor."  I will discuss current work with Vigleik Angelveit about including the higher homotopy groups: this gives the notion of a graded Tambara functor.  I will begin with a discussion of Mackey and Tambara functors before tackling the graded version.