The physics of voice is very complex and encompasses turbulent airflows interacting with vibrating, colliding and deforming bodies, like the vocal folds or the lips, and with acoustic waves propagating in a dynamic contorted vocal tract. Numerical approaches, and in particular the finite element method (FEM), have revealed as the most suitable option to solve many of those physical phenomena, and why not, attempting at a unified simulation, from muscle articulation and phonation to the emitted sound, in the mid-term. In this talk we will review some of the state of the art and current challenges in numerical voice production; from static and dynamic vowel sounds to sibilants and the self oscillations of the vocal folds. Numerical methods can be very appealing because they allow one not only to listen to a simulated sound but also to visualize the sound sources and the propagation of acoustic waves through the vocal tract. However, care should be taken not to use FEM as a black box. Even if a fully unified simulation of the whole process of voice generation was possible in an ideal supercomputer, would this reveal all the physics beneath voice production