  We discuss spatial dynamics and collapse scenarios of localized waves
governed by the nonlinear Schr\"{o}dinger equation with nonlocal nonlinearity.
Firstly, we prove that for arbitrary nonsingular attractive nonlocal nonlinear
interaction in arbitrary dimension collapse does not occur. Then we study in
detail the effect of singular nonlocal kernels in arbitrary dimension using
both, Lyapunoff's method and virial identities. We find that for for a
one-dimensional case, i.e. for $n=1$, collapse cannot happen for nonlocal
nonlinearity. On the other hand, for spatial dimension $n\geq2$ and singular
kernel $\sim 1/r^\alpha$, no collapse takes place if $\alpha<2$, whereas
collapse is possible if $\alpha\ge2$. Self-similar solutions allow us to find
an expression for the critical distance (or time) at which collapse should
occur in the particular case of $\sim 1/r^2$ kernels. Moreover, different
evolution scenarios for the three dimensional physically relevant case of Bose
Einstein condensate are studied numerically for both, the ground state and a
higher order toroidal state with and without an additional local repulsive
nonlinear interaction. In particular, we show that presence of an additional
local repulsive term can prevent collapse in those cases.
