This paper is about mapping strategies between gesture data and synthesis model parameters by means of perceptual spaces. We define three layers in the mapping chain: from gesture data to gesture perceptual space, from sound perceptual space to synthesis model parameters, and between the two perceptual spaces. This approach makes the implementation highly modular. Both perceptual spaces are developed and depicted with their features. To get a simple mapping between the gesture perceptual subspace and the sound perceptual subspace, we need to focus our attention on the two other mappings. We explain the mapping types: explicit/implicit, static/dynamic. We also present the technical and aesthetical limits introduced by mapping. Some practical examples are given of the use of perceptual spaces in experiments done at LMA in a musical context. Finally, we discuss several implications of the mapping strategies: the influence of chosen mapping limits onto performers' virtuosity, and the incidence of mapping on the learning process with virtual instruments and on improvisation possibilities.