We start by observing that there are numerous algebraic structures (Poisson algebras, Gerstenhaber algebras, various bialgebras and dialgebras) which consist of two operations and a certain interchange rule between these operations. In order to be `good,' such an interchange rule must be coherent in an appropriate sense, we call it then a distributive law. After explaining the meaning of the above mentioned coherence, we give a general recipe how to construct a cohomology theory (controling deformations) for a structure with a distributive law as a combination of cohomology theories of its constituents. The talk will be based on results of mine and Tom Fox of Montreal.