We will review connections between the stochastic and deterministic Growth Problems in 2 dimensions (such as Diffusion Limited Aggregation and Laplacian Growth Problem) and theory of finite and infinite dimensional integrable systems.

In particular, we will present our recent results relating the Elliptic Growth free boundary problems and theory of algebraically integrable Calogero-Moser type systems.

Finally, we'll discuss prospectives in finding correspondence between integrable statistical field models and DLA type problems.