Many a problem in combinatorial operations research (including, in particular, linear and nonlinear integer programming), can be formulated with the aid of real-valued functions with bivalent (0, 1) variables. This paper surveys the methods originated and developed by the authors for solving such problems. The procedures are presented here in an improved version; the most important improvements refer to linear bivalent programming, to the determination of the “basic solutions,” etc. No proofs are given; for these as well as for various applications, the reader is referred to the authors' Boolean Methods in Operations Research and Related Areas.