The piano is a complicated, subtle tone-producing device. Much work has been done toward understanding its physical and acoustical mechanisms. On the other hand, excellent results have been achieved in commercial sound synthesis, particularly through the sampling and processing of real piano sounds. The present work builds on digital waveguide string synthesis methods to develop physics-based synthesis algorithms of piano and percussion sounds through appropriate physical models chosen with an eye toward psychoacoustics-based simplifications and toward mathematical reformulation into efficient, physically calibratible digital filter structures. Recently developed physics-based sound synthesis algorithms include: a shared-loss string coupling structure modeling two-stage decay, and a simplified string stiffness filter design, both calibratible from recorded sound data; a time-varying wave digital piano hammer or mallet filter directly modeling nonlinear felt stiffness and hysteresis; membrane, plate, room, and piano soundboard models using a 2-D, or 3-D digital waveguide mesh designed for high-speed multiply-free parallel hardware implementation; and a highly simplified commuted piano synthesis method, which commutes the high-order soundboard filter backward through the strings and linearized hammer filter, replacing it with its own impulse response, which in turn is synthesized directly with enveloped noise.