This paper reviews the current state of sampling theory 50 years after Shannon's formulation of the sampling theorem. It focuses on regular sampling, where samples are taken on a uniform grid. Recent research has revived interest in sampling, particularly through its connections with wavelet theory. The paper reinterprets Shannon's sampling theorem as an orthogonal projection onto the subspace of band-limited functions. It extends the standard sampling paradigm to more general "shift-invariant" function spaces, including splines and wavelets, allowing for simpler and more realistic interpolation models. The paper discusses the determination of approximation error and sampling rate for arbitrary input signals, and reviews variations of sampling such as wavelets, multiwavelets, Papoulis generalized sampling, finite elements, and frames. It also briefly mentions irregular sampling and radial basis functions. The paper emphasizes the importance of understanding the sampling process in the frequency domain and provides a geometrical Hilbert space interpretation of the sampling paradigm. It shows how the sampling theorem can be generalized to other function spaces and how the approximation error can be controlled. The paper concludes with a discussion of the practical implications of these results for signal processing and communications.This paper reviews the current state of sampling theory 50 years after Shannon's formulation of the sampling theorem. It focuses on regular sampling, where samples are taken on a uniform grid. Recent research has revived interest in sampling, particularly through its connections with wavelet theory. The paper reinterprets Shannon's sampling theorem as an orthogonal projection onto the subspace of band-limited functions. It extends the standard sampling paradigm to more general "shift-invariant" function spaces, including splines and wavelets, allowing for simpler and more realistic interpolation models. The paper discusses the determination of approximation error and sampling rate for arbitrary input signals, and reviews variations of sampling such as wavelets, multiwavelets, Papoulis generalized sampling, finite elements, and frames. It also briefly mentions irregular sampling and radial basis functions. The paper emphasizes the importance of understanding the sampling process in the frequency domain and provides a geometrical Hilbert space interpretation of the sampling paradigm. It shows how the sampling theorem can be generalized to other function spaces and how the approximation error can be controlled. The paper concludes with a discussion of the practical implications of these results for signal processing and communications.