This chapter targets a better understanding of the compositionality of analyses, including different forms of compositionality and specific conditions of composition. Analysis involves models, contexts, and properties. These are all expressed in languages with their own semantics. For a successful composition of analyses, it is therefore important to compose models as well as the underlying languages. We aim to develop a better understanding of what is needed to answer questions such as “When I want to compose two or more analyses, what do I need to take into account?” We describe the elements impacting analysis compositionality, the relation of these elements to analysis, and how composition of analysis relates to compositionality of these elements. This core chapter addresses Challenge 1 introduced in Chapter 3 of this book (the theoretical foundations—how to compose the underlying languages, models, and analyses).