In the review article we sum up the results of development of Skyrme's solitonic approach in the baryon structure description. Contrary to the already existing literature in the field we pay a special tribute not to pragmatical aspects or the model, but rather to initial ideas, deep topological content and to such delicate problems as an existence or solutions, attainability of the energy absolute minimum of the hedgehof ansatz and so on. Exactly these features of Skyrme's approach are to the authors opinion the main-advantages in contrast to other schemes used in the strong interaction physics. The collected material will provide the reader with a deeper understanding of the Skyrme model structure and special features, as well as might serve as a bose for further modifications and development of more, realistic scenario for processes in the low energy QCD. The necessity of the latter is quite obvious 4 figs. 132 refs (152 titles.).