  Recent breakthroughs in the creation of ultra-cold atomic gases in the
laboratory have ushered in major changes in physical science. Many novel
experiments are now possible, with an unprecedented control of interaction,
geometry and purity. Quantum many-body theory is facing severe challenges in
quantitatively understanding new experimental results. Here, we review some
recently developed theoretical techniques that provide successful predictions
for density response of a strongly correlated atomic Fermi gas. These include
the strong-coupling random-phase approximation theory, high-temperature quantum
virial expansion, and asymptotically exact Tan relations applicable at large
momentum.
