Before an exoplanet transit, atmospheric refraction bends light into the line of sight of an observer. The refracted light forms a stellar mirage, a distorted secondary image of the host star. I model this phenomenon and the resultant out-of-transit flux increase across a comprehensive exoplanetary parameter space. At visible wavelengths, Rayleigh scattering limits the detectability of stellar mirages in most exoplanetary systems with semi-major axes $lesssim$6 AU. A notable exception is almost any planet orbiting a late M or ultra-cool dwarf star at $gtrsim$0.5 AU, where the maximum relative flux increase is greater than 50 parts-per-million. Based partly on previous work, I propose that the importance of refraction in an exoplanet system is governed by two angles: the orbital distance divided by the stellar radius and the total deflection achieved by a ray in the optically thin portion of the atmosphere. Atmospheric lensing events caused by non-transiting exoplanets, which allow for exoplanet detection and atmospheric characterization, are also investigated. I derive the basic formalism to determine the total signal-to-noise ratio of an atmospheric lensing event, with application to Kepler data. It is unlikely that out-of-transit refracted light signals are clearly present in Kepler data due to Rayleigh scattering and the bias toward short-period exoplanets. However, observations at long wavelengths (e.g., the near-infrared) are significantly more likely to detect stellar mirages. Lastly, I discuss the potential for the Transiting Exoplanet Survey Satellite to detect refracted light and consider novel science cases enabled by refracted light spectra from the James Webb Space Telescope.
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