A more recent area of inquiry in the field of harmonic analysis has been the search for analogs of the Whittaker–Kotel' nikov– Shannon sampling series for noncommutative groups. This chapter explores this question within the context of the discretization problem. It revisits the notion of admissible representations. The chapter delves into a methodology based on oscillation estimates, owing to Gröchenig and Fuhr, for discretizing an admissible representation to construct frames. It expands the concept of bandlimitation on the real line, as exemplified by Paley–Wiener-type spaces, to a broader class of noncommutative Lie groups and provides sufficient conditions under which the discretization problem admits a favorable resolution. The chapter also provides us with powerful tools to detect relevant features of representations, allowing the existence of a class of functions called continuous frames or generalized wavelets.