  The importance of the tensor force for nuclear structure has been recognized
long ago. Recently, the interest for this topic has been revived by the study
of the evolution of nuclear properties far from the stability line. However, in
the context of the effective theories that describe medium-heavy nuclei, the
role of the tensor force is still debated. This review focuses on ground-state
properties like masses and deformation, on single-particle states, and on
excited vibrational and rotational modes. The goal is to assess which
properties, if any, can bring clear signatures of the tensor force within the
mean-field or density functional theory framework. It will be concluded that,
while evidences for a clear neutron-proton tensor force exist despite
quantitative uncertainties, the role of the tensor force among equal particles
is less well established.
