  We present a pairing fluctuation theory which self-consistently incorporates
finite momentum pair excitations in the context of BCS--Bose-Einstein
condensation (BEC) crossover, and we apply this theory to high $T_c$
superconductors and ultracold Fermi gases. There are strong similarities
between Fermi gases in the unitary regime and high Tc superconductors. Here we
address key issues of common interest, especially the pseudogap. In the Fermi
gases we summarize recent experiments including various phase diagrams (with
and without population imbalance), as well as evidence for a pseudogap in
thermodynamic and other experiments.
