Holomorphic bundles over elliptic curves and integrable systems

We review classification of elliptic integrable systems based on the underlying holomorphic bundles over punctured elliptic curves. Different examples of integrable systems arise according to certain data of the bundles including some characteristic class similar to degree of a vector bundle. Examples include the Calogero-Moser and Gaudin type models, Euler-Arnold tops, interacting tops etc.