Pertinent simulations of string instruments, for the purpose of sound synthesis or instrument making, require at least three major conditions: a deep understanding of the physics, accurate measurements of elastic and geometric properties, and good mathematical properties of the discrete time modeling. Today, the modeling of complete string instruments appears to be a rather unrealistic objective. However, one intermediate step consists of a thorough investigation of the vibrations and radiation of plates, which are essential in the production of sound by such sources. This presentation will concentrate first on the development of appropriate damping models for both isotropic and anisotropic plates, using a generalized viscoelastic formulation, in order to account for the complex, but clearly audible, influence of frequency-dependent decay times on timbre of most materials. Other refinements, such as the time-domain modeling of inhomogeneities, stiffening of plates, and plate--cavity coupling, which are known to be significant in the physics of string instruments, will be addressed. Sound examples will be played, highlighting the results and limits of the state of the art for these current investigations.