Various scenarios for self-organization in a wide range of nonequilibrium physical, chemical, and biological systems are examined. It is stressed that in many systems small-amplitude dissipative structures never form: At the instant at which the homogeneous state stratifies, large-amplitude dissipative structures appear abruptly. These large-amplitude structures are striations, spots, or blobs. Methods for the construction of such dissipative structures and for studying their stability are discussed for an arbitrary departure of the system from equilibrium. Many self-organization scenarios do not involve an instability of the dissipative structures of a given type and are instead determined by a local breakdown effect. In real systems, self-organization is determined by the spontaneous appearance and subsequent evolution of autosolitons (localized dissipative structures). The conditions under which turbulence arises in such systems in the absence of a flow are discussed. This turbulence is a complicated picture of the random appearance and disappearance of interacting autosolitons in various parts of the system. In gaseous and semiconductor plasmas, dissipative structures can arise in the form of numerous current filaments or electric-field domains. Their formation is unrelated to the shape of the current-voltage characteristic of the system. There is a discussion of certain self-organization phenomena in systems in which static dissipative structures may be accompanied by pulsating dissipative structures and autowaves. Corresponding effects in systems with flows (or fluxes of material) are also discussed. The general results of self-organization theory are used to explain the properties of the dissipative structures which have been observed and studied in numerical and experimental studies of physical systems of various types in recent years.