  Strongly correlated Fermi system plays a fundamental role in very different
areas of physics, from neutron stars, quark-gluon plasmas, to high temperature
superconductors. Despite the broad applicability, it is notoriously difficult
to be understood theoretically because of the absence of a small interaction
parameter. Recent achievements of ultracold trapped Fermi atoms near a Feshbach
resonance have ushered in enormous changes. The unprecedented control of
interaction, geometry and purity in these novel systems has led to many
exciting experimental results, which are to be urgently understood at both low
and finite temperatures. Here we review the latest developments of virial
expansion for a strongly correlated Fermi gas and their applications on
ultracold trapped Fermi atoms. We show remarkable, quantitative agreements
between virial predictions and various recent experimental measurements at
about the Fermi degenerate temperature. For equation of state, we discuss a
practical way of determining high-order virial coefficients and use it to
calculate accurately the long-sought third-order virial coefficient, which is
now verified firmly in experiments at ENS and MIT. We discuss also virial
expansion of a new many-body paramter - Tan's contact. We then turn to less
widely discussed issues of dynamical properties. For dynamic structure factor,
the virial prediction agrees well with the measurement at the Swinburne
University of Technology. For single-particle spectral function, we show that
the expansion up to the second order accounts for the main feature of
momentum-resolved rf-spectroscopy for a resonantly interacting Fermi gas, as
recently reported by JILA. In the near future, more practical applications with
virial expansion are possible, owing to the ever-growing power in computation.
