We review a novel approach to treating many-body effects in diffusion-limited
kinetics. The derivation of the general expression for the survival probability of
a Brownian particle in the presence of randomly distributed traps is given. The
reduction of this expression to both the Smoluchowski solultion and the well-
known asymptotic behavior is demonstrated. It is shown that the Smoluchowski
solution gives a lower bound for the particle survival probability. The correction
to the Smoluchowski solution which takes into account the particle death
slowdown in the initial process stage is described. The steady-state rate-constant
concentration dependence and the reflection of many-body effects in it are
discussed in detail.