Ever since the time of Boltzmann. the desire to understand how macroscopic irreversible behavior arises out of the complexity of the underlying microscopic processes has been driving the development of the statistical mechanical theory of many-body systems. While most of the "fundamental" questions associated with irreversible processes have yet to be answered to the satisfaction of all physicists, the theory has obtained valuable results for "down-to-earth" physics by giving molecular expression for those quantities encountered in macroscopic evolution laws. Most of those questions concerning the general form of macroscopic evolution equations, their features and symmetries, and their connection with the molecular process can be answered quite generally, independent of particular models, on different levels of approximation, each level being related to the others by a hierachical structure.