  In high energy physics, the luminosity is one useful value to characterize
the performance of a particle collider. To gain more available data, we need to
maximize the luminosity in most collider experiments. With the discussions of
tune shift involved the beam dynamics and a recently proposed "crabbed waist"
scheme of beam-beam collisions, we present some qualitative analysis to
increase the luminosity. In addition, beam-beam tune shifts and luminosities of
$e^{+}e^{-}$, $pp$/$p\bar{p}$, and $\mu^{+}\mu^{-}$ colliders are discussed.
