Searching for materials with improved or perhaps completely novel properties involves an iterative process intended to successively narrow the gap between some initial starting point and the desired design target. This can be viewed as an optimization problem in a high-dimensional search space, often with many dozens of material parameters that need to be tuned. To tackle this, the evolutionary process in biology has been a source of inspiration in developing effective search algorithms. However, reaping the full benefits of bioinspired searches for materials design requires some thought. Here, we go beyond traditional black box algorithms and take a broader view of computational evolution strategies. We discuss recent strategies that exploit knowledge about the material configuration statistics and we highlight the advantages when time-varying environments are considered. Throughout, we emphasize that the search strategies themselves can be viewed as a nonequilibrium dynamical process in design space.