Digital waveguide physical modeling offers efficient simulation of acoustic wave propagation as compared to general finite-difference schemes commonly used in computational physics. This efficiency has enabled the real-time implementation of physically modeled musical instruments and sound effects, as well as real-time vocal models and artificial reverberation. This paper provides an overview of the historical evolution and applications of digital waveguide modeling and highlights recent advances in the field. Parametric optimization using classical, evolutionary and neural approaches are also discussed and compared. Digital waveguides provide physically accurate simulations with reduced computational cost, and can now be optimized with modern machine learning and differentiable digital signal processing techniques.