I found the notion of “thick” morphisms of (super)manifolds several years ago, in search of a construction of L∞-morphisms of homotopy Poisson brackets. Ordinary maps cannot give interesting L∞-morphisms because pull-backs of functions by them are algebra homomorphisms — in particular, linear, — while nontrivial L∞-morphisms have to be nonlinear. The essential feature of thick morphisms is that they induce nonlinear pull-backs of functions. In the talk, Iwill give the definition of thick morphisms and describe their properties.