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In this survey we present the near-optimal stochastic control problemaccording to some recent tools in the literature. In particular, we focus onthe approach of a discretization of the noise values instead of the canonicaltime-discretization. This is the so called {\it skeleton} structure. Thisallows to obtain an $\epsilon$-optimal control in non-Markovian systems (themain Theorem). A simple example illustrates the technique. The importance ofthe approach is emphasised in a final section on open problems related to moregeometrical framework and discontinuous noise.

Stochastic near-optimal control: additive, multiplicative, non-Markovian and applications