The FPP Conjecture of Adams, van Leeuwen, Miller, and Vogan proposes a strong upper bound on the set of irreducible unitary representations of a real reductive group (such as GL_n(R)). In this talk, I will review what is known about the structure and shape of the unitary dual and then sketch a short proof of the FPP conjecture. This is based on recent joint work with Dougal Davis.