The outlines of a recently developed model of a grand piano are summarized. Using dedicated numerical methods, the main vibratory and acoustic variables of each constitutive part of the instrument (strings, bridge, soundboard, sound pressure) are simulated in the time-domain. The obtained waveforms are analyzed and compared with experimental data derived from measurements on a Steinway D grand piano. This comparison yields valuable insight into the physics of the instrument. It shows, in particular, that a nonlinear string model is necessary to account for the observed richness of piano spectra. The model is able to reproduce important features of piano sounds, such as the presence of soundboard modes in the transients, precursors and phantom partials. However, one important limitation of the model, in its present state, is that it does not account for the change of polarization observed on piano strings. Experimental observations of this phenomenon are discussed and a preliminary model for explaining the possible role of the zig-zag end condition in string polarization change is presented.