The concept of emergence is used in a variety of scientific fields and disciplines to denote an even wider variety of phenomena. This has resulted in a plethora of perspectives and treatments. The diversity of phenomena going under the moniker of emergence raises the question of what these phenomena have in common and whether different types of emergence can be distinguished on general grounds. Since emergence is recognised in so many different fields as a relevant concept, it would be useful to have a general conceptual framework that allows a treatment of emergence without explicit reference to the specific underlying mechanism. This article aims to provide a general framework in which emergence can be addressed. For this a new concept, the conjugate, is introduced and the place of the observer relative to the system is given a renewed appreciation. Since the framework abstracts from the underlying interactions, emergence in different types of systems can be compared and discussed on equal terms. Reframing emergence in this way leads to a typology of emergences that is both illuminating and integrative. In the elaboration the concepts and different types of emergence are discussed and compared with other treatments and typologies of emergence in the literature. Examples from various fields are given to illustrate the theoretical discourse. Furthermore applications of the concepts and typology to social systems, evolution, and co-evolution in ecosystems will be given It will be concluded that many apparently different views and treatments of emergence can be restated and compared within the framework presented in this article.