  In this paper we review some results of our works on the magnetization
processes in: i) Isolated nanomagnets, both in the one-spin approximation and
as many-spin systems. Here, we focus on the intrinsic properties, e.g., those
induced by finite-size, boundary and surface effects. We also investigate the
crossover between the two regimes. ii) Assemblies of nanomagnets, also in the
two situations. We focus on their behavior mainly due to dipole-dipole
interactions. Then, we will comment on the interplay between these intrinsic
and collective effects.
