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The class of almost periodic functions was introduced by the Danish mathematician H. Bohr around 1924-1926 and later investigated by a great number of other authors. Any Bohr almost periodic function is continuous, which does not hold for the generalized almost periodic functions considered in the pioneering papers of V. Stepanov, A. S. Besicovitch and H. Weyl. The notion of an almost automorphic function was introduced by S. Bochner in 1955 and extensively studied by many authors later. Any almost periodic function is almost automorphic, while the converse statement fails to be true. In this talk, we will present the main denitions and results about almost periodic functions and their applications to the abstract Volterra integro-differential equations.