  Adaptive perturbation is a new method for perturbatively computing the
eigenvalues and eigenstates of quantum mechanical Hamiltonians that are widely
believed not to be solvable by such methods. The novel feature of adaptive
perturbation theory is that it decomposes a given Hamiltonian, $H$, into an
unperturbed part and a perturbation in a way which extracts the leading
non-perturbative behavior of the problem exactly. In this talk I will introduce
the method in the context of the pure anharmonic oscillator and then apply it
to the case of tunneling between symmetric minima. After that, I will show how
this method can be applied to field theory. In that discussion I will show how
one can non-perturbatively extract the structure of mass, wavefunction and
coupling constant
