We present an overview of Davydov's theory of charge and energy transfer in quasi-one-dimensional molecular crystals. Elucidation of its relevance for the transport properties of biological macromolecules: α-helix proteins and DNA have been studied in detail. The validity of the Davydov model is discussed within the general theory of self-trapping phenomena. Different types of self-trapped states were identified for the particular region's system parameter space. Various types of self-trapped states are classified for different values of basic system parameters. Finally, we discuss the viability of the soliton theory of charge and energy transfer.