Nature's spectacular inventiveness, reflected in the enormous diversity of form and function displayed by the biosphere, is a feature of life that distinguishes living most strongly from nonliving. It is, therefore, not surprising that this aspect of life should become a central focus of artificial life. We have known since Darwin that the diversity is produced dynamically, through the process of evolution; this has led life's creative productivity to be called Open-Ended Evolution (OEE) in the field. This article introduces the first of two special issues on current research on OEE and on the more general concept of open-endedness. Most of the papers presented in these special issues are elaborations of work presented at the Third Workshop on Open-Ended Evolution, held in Tokyo as part of the 2018 Conference on Artificial Life.