OPTICAL resonators are essential components of lasers and other optical devices, A resonator is characterized by a set of modes, each with a resonant frequency omega and resonance width delta omega = 1/tau, where tau is the lifetime of a photon in the mode, Cylindrical or spherical dielectric resonators have extremely long-lived resonances(1) due to ’whispering gallery’ modes in which light circulates around the perimeter trapped by total internal reflection, These resonators emit light isotropically, Recently a new category of asymmetric resonant cavities has been proposed in which substantial deformation of the cavity from cylindrical or spherical symmetry leads to partially chaotic ray dynamics, This has been predicted(2-4) to give rise to a universal, frequency-independent broadening of the,whispering-gallery resonances, and to highly anisotropic emission, Here we present solutions of the wave equation for asymmetric resonant cavities which confirm these predictions but also reveal interesting frequency-dependent effects characteristic of quantum chaos, For small deformations the lifetime is controlled by evanescent leakage, the optical analogue of quantum tunnelling(5); here the lifetime is significantly shortened by a process known as ’chaos-assisted tunnelling’(6-7). In contrast, for large deformations (similar to 10%) some resonances are found to have longer lifetimes than predicted by the ray chaos model due to the phenomenon of ’dynamical localization’(8).