  Since the introduction of Dyson's Brownian motion in early 1960's, there have
been a lot of developments in the investigation of stochastic processes on the
space of Hermitian matrices. Their properties, especially, the properties of
their eigenvalues have been studied in great details. In particular, the
limiting behaviors of the eigenvalues are found when the dimension of the
matrix space tends to infinity, which connects with random matrix theory. This
survey reviews a selection of results on the eigenvalues of stochastic
processes from the literature of the past three decades. For most recent
variations of such processes, such as matrix-valued processes driven by
fractional Brownian motion or Brownian sheet, the eigenvalues of them are also
discussed in this survey. In the end, some open problems in the area are also
proposed.
