  We give a brief review of two nonperturbative phenomena typical of
noncommutative field theory which are known to lead to the perturbative
instability known as the UV-IR mixing. The first phenomena concerns the
emergence/evaporation of spacetime geometry in matrix models which describe
perturbative noncommutative gauge theory on fuzzy backgrounds. In particular we
show that the transition from a geometrical background to a matrix phase makes
the description of noncommutative gauge theory in terms of fields via the Weyl
map only valid below a critical value g_*. The second phenomena concerns the
appearance of a nonuniform ordered phase in noncommutative scalar \phi^4 field
theory and the spontaneous symmetry breaking of translational/rotational
invariance which happens even in two dimensions. We argue that this phenomena
also originates in the underlying matrix degrees of freedom of the
noncommutative field theory. Furthermore it is conjectured that in addition to
the usual WF fixed point at $\theta=0$ there must exist a novel fixed point at
\theta=\infty corresponding to the quartic hermitian matrix model.

High Energy Physics - Theory;General Relativity and Quantum Cosmology;High Energy Physics - Lattice;High Energy Physics - Phenomenology