[en] The various models that were successively developed for describing static nuclear deformations are reviewed. The properties of the nuclei in their ground state lead to the concept of ellipsoidal nuclei, the liquid drop model being intended to explain the deformations of the excited nucleus, the shell corrections explain the drawbacks of the liquid drop model and the Strutinski theory describes their effects on the fission barrier. The collective model, the deformed shell model and the unified model having been successively introduced to explain the rotational spectrum. The approximations involving infinite nuclear matter and effective interactions, and nuclear Hartree-Fock calculations are briefly outlined jointly with heavy ion excitation of yrast levels