  Brownian motion has played important roles in many different fields of
science since its origin was first explained by Albert Einstein in 1905.
Einstein's theory of Brownian motion, however, is only applicable at long time
scales. At short time scales, Brownian motion of a suspended particle is not
completely random, due to the inertia of the particle and the surrounding
fluid. Moreover, the thermal force exerted on a particle suspended in a liquid
is not a white noise, but is colored. Recent experimental developments in
optical trapping and detection have made this new regime of Brownian motion
accessible. This review summarizes related theories and recent experiments on
Brownian motion at short time scales, with a focus on the measurement of the
instantaneous velocity of a Brownian particle in a gas and the observation of
the transition from ballistic to diffusive Brownian motion in a liquid.
