Since its inception, evolutionary theory has experienced a number of extensions. The most important of these took the forms of the Modern Evolutionary Synthesis (MES), embracing genetics and population biology in the early 20th century, and the Extended Evolutionary Synthesis (EES) of the last thirty years, embracing, among other factors, non-genetic forms of inheritance. While we appreciate the motivation for this recent extension, we argue that it does not go far enough, since it restricts itself to widening explanations of adaptation by adding mechanisms of inheritance and variation. Here we argue that a more thoroughgoing extension is needed, one that broadens the explanatory scope of evolutionary theory. In addition to adaptation and its various mechanisms, evolutionary theory must recognize as a distinct intellectual challenge the origin of what we call “historical kinds.” Under historical kinds we include any process that acquires a quasi-independent and traceable lineage-history in biological and cultural evolution. A limited number of historical kinds have been recognized in evolutionary biology, and corresponding research programs have been formed around them. The best characterized examples are biological species and genes. We propose that the conceptual category of historical kinds can and needs to be extended, and we develop the notion of a historical kind in a series of paradigmatic exemplars, from genes and cell types to rituals and music. The explanation of the origin of historical kinds should be a main objective of biological and cultural sciences.