Dynamics of many noisy systems often exhibit one or more widely separated time scales. It is often desirable to derive effective mathematical models, in the form of stochastic differential equations (SDEs), to describe these systems. In this talk, we consider effective SDEs describing the behavior of Langevin systems in the limits when natural time scales become very small. It turns out that for a large class of Langevin systems with state-dependent coefficients additional drift terms, called noise-induced drifts, appear in the effective SDEs. We discuss recent progress and provide some perspectives on the phenomena of noise-induced drift.