This article presents a high-level conceptual framework to help orient the discussion and implementation of open-endedness in evolutionary systems. Drawing upon earlier work by Banzhaf et al. (2016), three different kinds of open-endedness are identified: exploratory, expansive, and transformational. These are characterized in terms of their relationship to the search space of phenotypic behaviors. A formalism is introduced to describe three key processes required for an evolutionary process: the generation of a phenotype from a genetic description, the evaluation of that phenotype, and the reproduction with variation of individuals according to their evaluation. The formalism makes explicit various influences in each of these processes that can easily be overlooked. The distinction is made between intrinsic and extrinsic implementations of these processes. A discussion then investigates how various interactions between these processes, and their modes of implementation, can lead to open-endedness. However, an important contribution of the article is the demonstration that these considerations relate to exploratory open-endedness only. Conditions for the implementation of the more interesting kinds of open-endedness—expansive and transformational—are also discussed, emphasizing factors such as multiple domains of behavior, transdomain bridges, and non-additive compositional systems. In contrast to a traditional Darwinian analysis, these factors relate not to the generic evolutionary properties of individuals and populations, but rather to the nature of the building blocks out of which individual organisms are constructed, and the laws and properties of the environment in which they exist. The article ends with suggestions of how the framework can be used to categorize and compare the open-ended evolutionary potential of different systems, how it might guide the design of systems with greater capacity for open-ended evolution, and how it might be further improved.