Toric unstable resonators consisting of two annular mirrors of toroidal shape are analyzed using geometrical, diffractive, and asymptotic theory. Geometrical modes and eigenvalues are derived using nonuniform magnification theory. The eigenvalues are identical to those for strip resonators, while the mode intensities include a 1/r dependence. Diffractive modes and eigenvalues exhibit some of the geometrical properties and show that toric resonators have little azimuthal mode separation. First-order asymptotic theory shows that high spatial frequency oscillations in the diffractive modes are due to inner and outer edge waves, with the inner edge wave dominating.