Designing and controlling virtual characters endowed with expressive gestures requires the modeling of multiple processes, involving high-level abstract representations to low-level sensorimotor models. An expressive gesture is here defined as a meaningful bodily motion which intrinsically associates sense, style, and expressiveness. The main challenges rely both on the capability to produce a large spectrum of parametrized actions executed with some variability in various situations, and on the biological plausibility of the motion of the virtual characters. The goals of the paper are twofold. First we review the different formalisms used to describe expressive gestures, from notations to computational languages. Secondly we identify and discuss remaining challenges in the generation of expressive virtual characters. The different models and formalisms are illustrated more particularly for theatrical and sign language gestures.