Abstract This paper contains the skeleton of one lecture, and of two raporteur's interventions, made at the Sanibel Symposium in February–March, 1979. The task asked of this lecturer was to present an outline of the program of nonequilibrium statistical mechanics, and to indicate some of the recent developments in our understanding of this program. Section I lists a few of the principal physical ingredients of the theory. The possible implementation of certain aspects of the program is demonstrated in Sec. II with the help of three exactly soluble models. Finally in Sec. III we extrapolate from these particular examples in two directions: the stochastic aspect of statistical mechanics, and some remarks on the theory of the quantum measurement process. The presence, at the Symposium, of several distinguished lecturers who presented their own original, and most interesting, contributions hopefully made appear less outrageous—at least at the time—the severe omissions due to the personal choices this particular speaker had to make to keep within the time limitations inherent to such a gathering. It is now hoped that, even when taken out of the full context of the Symposium, the rearranged text which follows might nevertheless help focusing attention on some of the important problems remaining to be solved. It is a pleasure to acknowledge here the stimulating hospitality of the Symposium Scientific Director, Professor P.‐O. Löwdin.