In a Hilbert space, a frame is a set of vectors that can be used to represent any vector in the space. In finite-dimensional vector spaces, a frame is simply a spanning set, a set of vectors that can be used to represent all the vectors in the space. This chapter shows that the concept of frame is a natural generalization of that of a basis, in the sense that any vector in the Hilbert space admits stable series expansions in terms of the elements of a fixed frame. The chapter formalizes “The Discretization Problem” of unitary representation of a connected Lie group to construct systems such as frames, Parseval frames, orthonormal, and Riesz bases. It discusses how this problem naturally arises in wavelet and time-frequency analyses. Furthermore, the chapter develops an approach that allows us to view these subjects as specific occurrences of a much deeper phenomenon.