  This article is written as a Lecture given in the 2006 Varenna Summer School
on "Ultracold Fermi Gases". Here we present a review of BCS--Bose Einstein
condensation (BEC) crossover theory with emphasis on finite temperature
effects. We discuss the role of temperature $T$ as it enters a theoretical
formalism which is based on the standard BCS-Leggett ground state. We also
discuss the role of temperature in the context of experiments ranging from
thermometric issues to signatures of superfluidity. Particularly important to
this discussion is the novel normal state associated with the crossover regime,
intermediate between BCS and BEC. The experimental evidence for this unusual
normal state (associated with pre-formed pairs) and its counterpart below $T_c$
(associated with non-condensed pairs) is presented in the context of different
experiments. We end with a discussion of finite temperature effects in spin
polarized superfluids, where $T$ is found to play a crucial role in both theory
and experiment.
