  In the lattice CP(N) models we studied the problems related to the measure of
the topological susceptibility and the string tension . We perfomed numerical
simulations at N=4 and N=10. In order to test the universality, we adopted two
different lattice formulations. Scaling and universality tests led to the
conclusion that at N=10 the geometrical approach gives a good definition of
lattice topological susceptibility. On the other hand, N=4 proved not to be
large enough to suppress the unphysical configurations, called dislocations,
contributing to the topological susceptibility. We obtained other
determinations of the topological susceptibility by the field theoretical
method, wich relies on a local definition of the lattice topological charge
density, and the cooling method. They gave quite consistent results, showing
scaling and universality. The large-N expansion predicts an exponential area
law behavior for sufficiently large Wilson loops, which implies confinement,
due to the dynamical matter fields and absence of the screening phenomenon. We
determined the string tension, without finding evidence of screening effects.
