As a result of their complexity and versatility, pianos are arguably one of the most important instruments in Western music. The size, weight, and price of grand pianos as well as their relatively simple control surface (i.e., the keyboard), have led to the development of digital counterparts that mimic the sound of acoustic pianos as closely as possible. While most commercial digital pianos are based on sample playback, it is also possible to reproduce a piano's sound by modeling the physics of the instrument. The process of physical modeling starts with first understanding the physical principles, followed by creating accurate numerical models, and finally, finding numerically optimized signal processing models that allow sound synthesis in real time by excluding inaudible phenomena and adding some perceptually important features by using signal processing tricks. Accurate numerical models can be used by physicists and engineers to understand how the instrument functions or to help piano makers with instrument development. On the other hand, efficient real-time models are geared toward composers and musicians who perform at home or onstage. This article provides an overview of a physics-based piano synthesis beginning with computationally heavy, physically accurate approach followed by a discussion of the approaches that are designed to produce the best possible sound quality for real-time synthesis.