The accuracy of single scale continuum physics models, usually solved by finite elements, involving complex material behavior is restricted mostly due to the necessity to use phenomenological material models, which oversimplify the actual material behavior. In computational homogenization, these material laws are replaced by a second model, which represents the microstructure, the properties of which thus directly determine the material behavior on the macroscale. The drawback of this approach is that the micro-model usually needs to be evaluated thousands or even millions of times to carry out only one macroscopic simulation, which is in many cases computationally unaffordable. Therefore, model reduction techniques are discussed in this talk to speed up the micro-model by several orders of magnitude while preserving a sufficient accuracy. Applications in different fields of continuum physics are presented, comparing several novel model order reduction approaches.