This paper provides an overview of the current state of sampling theory, 50 years after Shannon's formulation of the sampling theorem. The focus is on regular sampling, where the grid is uniform, and highlights recent advancements in the field, particularly the connection to wavelet theory. The authors reinterpret Shannon's sampling procedure as an orthogonal projection onto the subspace of band-limited functions and extend it to more general "shift-invariant" function spaces, including splines and wavelets. They discuss practical interpolation models and the use of non-ideal low-pass filters, and present results on determining the approximation error and optimal sampling rates for arbitrary input signals. The paper also reviews various extensions and variations of sampling, such as wavelets, multiwavelets, Papoulis generalized sampling, finite elements, and frames. The discussion covers both theoretical foundations and practical applications, making it a comprehensive resource for researchers and practitioners in signal processing and communications.This paper provides an overview of the current state of sampling theory, 50 years after Shannon's formulation of the sampling theorem. The focus is on regular sampling, where the grid is uniform, and highlights recent advancements in the field, particularly the connection to wavelet theory. The authors reinterpret Shannon's sampling procedure as an orthogonal projection onto the subspace of band-limited functions and extend it to more general "shift-invariant" function spaces, including splines and wavelets. They discuss practical interpolation models and the use of non-ideal low-pass filters, and present results on determining the approximation error and optimal sampling rates for arbitrary input signals. The paper also reviews various extensions and variations of sampling, such as wavelets, multiwavelets, Papoulis generalized sampling, finite elements, and frames. The discussion covers both theoretical foundations and practical applications, making it a comprehensive resource for researchers and practitioners in signal processing and communications.