Morse–Bott homology is a generalisation of Morse homology to functions with degenerate critical points in situations where symmetries occur. In this chapter, we introduce the definition of Morse–Bott homology via the cascade approach as for us the main motivation is to construct a homology theory associated with the twisted Rabinowitz action functional. Then we discuss analytical difficulties arising for defining a homology theory associated with a Morse–Bott function on finite-dimensional smooth manifolds.