The status of the microscopic theories is reviewed for the following types of order-disorder structural phase transitions in crystals: a) phase transitions in crystals with hydrogen bonds; b) orientational phase transitions in ionic-covalent crystals; c) orientational phase transitions in molecular crystals; d) order-disorder phase transitions in ordered interstitial and substitutional alloys. Attention is focused primarily on the static properties, i.e., the nature of the ordering, the phasetransition thermodynamics, and the distinctive features of these phase transitions in comparison with other phase transitions, particularly magnetic ones. The methods employed in the theoretical description of order-disorder structural phase transitions are examined--the Hamiltonians used, approximate methods for calculating the statistical properties (with allowance for correlation effects), exactly solvable models, etc. The existing theories of the phase transitions in various real crystals, including problems and results, are critically discussed for phase transitions of types a) and b).