Instantons are an important source of nonperturbative
effects in quantum field theories, but their role in asymptotically
free theories has not been well understood. In this talk, we will
present a new approach to instanton analysis in the context of 2d CP^N
sigma models. From this, we will show that, contrary to common
belief, instantons can in fact capture the vacuum structure and
non-perturbative properties such as mass gap, fractional theta
dependence, and confinement. In the supersymmetric sigma model,
our method gives a new derivation of the mirror symmetry and the
Landau-Ginzburg dual theory. Our construction also demonstrates
that there is no conflict between large N and instantons.