Higher spin gravity theories in Anti-de Sitter space have been conjectured to be holographically dual to conformal field theories with vector-like matter fields: in the simplest version of the duality, these are just free CFT's of N-component massless scalars or fermions. After reviewing these conjectures, I will discuss recent new tests of the duality based on comparing the bulk and boundary partition functions. In particular, I will show that the sum over one loop free energies of the infinite set of massless higher spin gauge fields in AdS_{d+1} is precisely consistent with the form of the O(N^0) term in the partition function of the CFT on S^d and S^1xS^{d-1}.