In the framework of a systematic approach, the present status of the problem of instanton-like transitions in high energy particle collisions is reviewed. The arguments in favor of the exponential form of the total two-particle cross section in the one-instanton sector, exp[1/g2F(E/E(sph))], are summarized. The perturbative technique for the evaluation of the function F(E/E(sph)) is considered in detail. The nonperturbative semiclassical approach to the evaluation of F(E/E(sph)), which may provide a reasonable basis for the numerical study of the problem, is discussed.