Computations in RO(G)-graded Bredon cohomology can be challenging and are not well understood, even for G=C₂, the cyclic group of order two. In this talk I will present a structure theorem for RO(C₂)-graded cohomology with constant Z/2 coefficients that substantially simplifies computations. The structure theorem says the cohomology of any finite C₂-CW complex decomposes as a direct sum of two basic pieces: shifted copies of the cohomology of a point and shifted copies of the cohomologies of spheres with the antipodal action. I will give some examples and sketch the proof, which depends on a Toda bracket calculation.