In eukaryotic cells, membrane compartments are split into two by membrane fission. This ensures discontinuity of membrane containers and thus proper compartmentalization. The first proteic machinery implicated in catalyzing membrane fission was dynamin. Dynamin forms helical collars at the neck of endocytic buds. This structural feature suggested that the helix of dynamin could constrict in order to promote fission of the enclosed membrane. However, verifying this hypothesis revealed itself to be a challenge, which inspired many in vitro and in vivo studies. The primary goal of this review is to discuss recent structural and physical data from biophysical studies that have refined our understanding of the dynamin mechanism. In addition to the constriction hypothesis, other models have been proposed to explain how dynamin induces membrane fission. We present experimental data supporting these various models and assess which model is the most probable.