  The pairing and superfluid phenomena in a two-component Fermi gas can be
strongly affected by the population and mass imbalances. Here we present phase
diagrams of atomic Fermi gases as they undergo BCS--Bose-Einstein condensation
(BEC) crossover with population and mass imbalances, using a pairing
fluctuation theory. We focus on the finite temperature and trap effects, with
an emphasis on the mixture of $^{6}$Li and $^{40}$K atoms. We show that there
exist exotic types of phase separation in the BEC regime as well as
sandwich-like shell structures at low temperature with superfluid or
pseudogapped normal state in the central shell in the BCS and unitary regimes,
especially when the light species is the majority. Such a sandwich-like shell
structure appear when the mass imbalance increases beyond certain threshold.
Our result is relevant to future experiments on the $^6$Li--$^{40}$K mixture
and possibly other Fermi-Fermi mixtures.
