These last years, deformable models raised much interest and found various applications in the field of computer vision. They provide an extensible framework to reconstruct shapes. Deformable surfaces, in particular, are used to represent 3D objects. They have been used for pattern recognition [47,2], computer animation [118], geometric modelling [40,75], simulation [45], boundaries tracking [14], segmentation [83], etc. In this report we propose a deformable surfaces survey. Many surface representation have been proposed to meet different 3D reconstruction problem requirements. We try to classify the main representations proposed in the literature and we study the effect of the representation on the model evolution behavior, revealing some similarities between different approaches. Whe then focus on a powerful discrete mesh representation, the simplex meshes. We propose different algorithms to control simplex meshes shape and topology. Whe show results on 3D medical images segmentation.