Various theoretical approaches to the calculation of the momentum distribution of a normal Fermi liquid are presented, discussed and compared. Particular attention is devoted to the Migdal-Luttinger theorem, which states that the momentum distribution is discontinuous at the Fermi momentum, the size of the discontinuity being equal to the quasiparticle strength at the Fermi surface. A proof of this theorem is given in terms of the spectral function; it also enables us to discuss the asymptotic behaviour of the derivative of the momentum distribution near the Fermi momentum. We show that most approximation schemes do not fulfill the Migdal-Luttinger theorem and do not ensure conservation of the number of particles. A "derivative expansion" is developed in which the momentum distribution is expressed in terms of energy derivatives of the mass operator. This expansion yields approximations which are compatible with the Migdal-Luttinger theorem. Examples are worked out in which the mass operator is expanded up to second and third order in the strength of the two-body interaction, or up to second order in the strength of Brueckner's reaction matrix; the latter case is of particular interest for nuclear matter. These examples illustrate the main features of the derivative expansion. They also enable one to exhibit its analogies and differences with two other main approaches. namely: (i) that which is based on the relationship between the momentum distribution and the spectral function, and (ii) the linked-cluster perturbation expansion of the momentum distribution in powers of the strength of the two-body interaction. It is outlined how one can construct approximations which conserve the total number of particles. The various approaches introduce, either implicitly or explicitly, an "auxiliary potential" that the nucleons are assumed to feel in the zero-order approximation. Our study sheds new light on the relevance of requiring that this auxiliary potential must be a continuous function of the momentum and be self-consistent at the Fermi surface. We demonstrate that, in order to recover the correct asymptotic behaviour for the derivative of the momentum distribution near the Fermi surface, it is moreover necessary that the derivative of the auxiliary potential be continuous and self-consistent at the Fermi surface. These requirements are shown to be badly violated in choices of the auxiliary potential that were previously proposed on the basis of a criterion of "maximum cancellation of diagrams".
