  We discuss the Sasakian geometry of odd dimensional homotopy spheres. In
particular, we give a completely new proof of the existence of metrics of
positive Ricci curvature on exotic spheres that can be realized as the boundary
of a parallelizable manifold. Furthermore, it is shown that on such homotopy
spheres $\scriptstyle{\Sigma^{2n+1}}$ the moduli space of Sasakian structures
has infinitely many positive components determined by inequivalent underlying
contact structures. We also prove the existence of Sasakian metrics with
positive Ricci curvature on each of the known $\scriptstyle{2^{2m}}$ distinct
diffeomorphism types of homotopy real projective spaces in dimension $4m+1$.
