In this chapter we present several basic notions and results regarding suspension flows, as a preparation for many developments in later chapters. We note that any smooth flow with a hyperbolic set gives rise to a suspension flow (see Chap. 3). In particular, we present the notions of cohomology and of Bowen–Walters distance. It happens that one can often describe the properties of a suspension flow in terms of corresponding properties in the base. This relation is considered in this chapter for the notion of cohomology. Several other relations of a similar type will be considered later in the book.