In this contribution we have considered the main items of the history of ideas on the structure of condensed solid matter. They are divided into two principal groups; one is based on discreteness (numbers, atoms), the other on continuity (geometrical figures). The evolution of these ideas has led to such notion as crystals, long-range and short-range order, continuous and discrete space, quasicrystals, types of disorder, amorphous structure. In its turn the new notions generated new theories, such as group theory, topology, etc. Significant attention was given to molecular dynamics, a new powerful instrument for solution of many problems connected with the structure of disordered phases. Leaning on a molecular dynamics, we have developed the theory of deformation and fracture for amorphous materials.