The problems of a possible curvature dependence of surface tension and its effect on the general scenario of nucleation processes are investigated. It is shown that practically all particular expressions for the curvature dependence of the surface tension of droplets (and bubbles) in one-component vapors (liquids) proposed so far may be obtained from one general ansatz for the Tolman coefficient by assigning appropriate values to two parameters, Moreover, criteria are given for determining the conditions under which the results can be extended to multicomponent systems, Based on these results it is shown that the account of a curvature dependence of surface tension may indeed result in significant variations of the work of formation of critical clusters, although a number of attempts made so far in determining this effect can be considered only as approximations, However, in contrast to earlier expressed opinions we show that at present no convincing evidence exists allowing a conclusion that the account of a curvature dependence of surface tension may lead to qualitative changes of the scenario of nucleation processes as characterized first by Gibbs and used as a starting point in practically all theories of homogeneous nucleation.