The question of predicting the long-term evolution of a mechanical structure in operation (e.g. fatigue) faces the associated issue of computational cost, particularly when the problem requires to be solved in the time domain (e.g. to account for the history of loads applied on the structure). When fast phenomena have to be described for a very long time interval, a scale separation assumption allows the use of time homogenization methods such as in [Guennouni & Aubry 1986], [Oskay & Fish ] or [Puel & Aubry 2014], which are based on a quasi-periodicity assumption. When environmental loads can be described by fast stochastic processes, a stochastic time homogenization framework can be defined and be seen as a transposition to time of the classical stochastic space homogenization method [Sab 1992]. The time-homogenized equations are determined by calculating the expectation of the different quantities, allowing to separate slow-evolving phenomena from fast-time components, as in [Puel & San 2016]. The main difficulty is then to substitute to the ensemble expectations a time average over a suitable time interval in order to derive the time-homogenized equations. The aim of the talk is to give theoretical as well as practical insights of this specific method. Examples will focus on structures with typical nonlinear material behaviors (e.g. viscoplasticity or damage), with loadings that can be described as the superposition of a slow deterministic component and a fast stochastic component, and equations that are solved in a quasi-static framework or in a fully dynamic framework.