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Let G be a finite group, p a prime number and k an algebraically closed field of characteristic p. Modular representation theory of finite groups aims to understand the blocks of kG which are the indecomposable two-sided ideals of the group algebra kG. To achieve this aim many categorical equivalences between module categories of the block algebras are introduced. Among these, we are concerned with the stable equivalence of Morita type. In this talk after a brief introduction to the subject, the role of Scott modules in this picture will be discussed. Then a recent result with a joint work with S. Koshitani among these lines will be presented.