Usual numerical methods become inefficient when they areapplied to highly oscillatory evolution problems (order reduction or completeloss of accuracy). The numerical parameters must indeed be adapted to the high frequencies that come into play to correctly capture the desired infor-mation, and this induces a prohibitive computational cost. Furthermore, thenumerical resolution of averaged models, even at high orders, is not sufficientto capture low frequencies and transition regimes. We present (very briefly)two strategies allowing to remove this obstacle for a large class of evolutionproblems: a 2-scale method and a micro/macro method. Two differentframeworks will be considered: constant frequency, and variable - possibly vanishing - frequency. The result of these approaches is the construction ofnumerical schemes whose order of accuracy no longer depends on the frequency of oscillation, one then speaks of uniform accuracy (UA) for these schemes. Finally, a new technique for systematizing these two methods willbe presented. Its purpose is to reduce the number of inputs that the user must provide to apply the method in practice. In other words, only the valuesof the field defining the evolution equation (and not its derivatives) are used.These methods have been successfully applied to solve a number of evolutionmodels: non-linear Schrdinger and Klein-Gordon equations, Vlasov-Poissonkinetic equation with strong magnetic field, quantum transport in graphene.