The nature of the normal phase of an ultracold Fermi gas in the BCS-BEC crossover regime is an interesting and unresolved question. As interactions increase, while the many-body ground state remains a condensate of paired fermions, the normal state must evolve from a Fermi liquid to a Bose gas of molecules. In this talk, I present a technique to spatially select a homogeneous sample from the center of a trapped gas to explore this crossover. Combining this technique with RF spectroscopy, we locally measure Tan's contact as a function of temperature and compare to various many-body theories. In another experiment, we measure the distribution of single-particle energies and momenta for a normal gas across the BCS-BEC crossover. We find that the data fit well to a two-part function that includes a peak corresponding to fermionic quasiparticles and an "incoherent background" that is modeled using the dispersion of thermal molecules. I also describe the construction of a new-generation Fermi gas apparatus.