We develop a mathematical theory to explain the mechanism of super-resolution in resonant media which consists of sub-wavelength resonators. Examples includes: Helmholtz resonators, plasmonic particles, and bubbles. For the media consists of small finite number of resonators, we show that super-resolution is due to sub-wavelength propagating modes; for the case of large number of resonators, we derive an effective media theory and show that super-resolution is due to the effective high contrast in the wave speed.