  This paper is a short review of the connection between certain types of
growth processes and the integrable systems theory, written from the viewpoint
of the latter. Starting from the dispersionless Lax equations for the 2D Toda
hierarchy, we interpret them as evolution equations for conformal maps in the
plane. This provides a unified approach to evolution of smooth domains (such as
Laplacian growth) and growth of slits. We show that the L\"owner differential
equation for a parametric family of conformal maps of slit domains arises as a
consistency condition for reductions of the dispersionless Toda hierarchy. It
is also demonstrated how the both types of growth processes can be simulated by
the large $N$ limit of the Dyson gas picture for the model of normal random
matrices.
