Context. Refraction deflects photons that pass through atmospheres, which affects transit light curves. Refraction thus provides an avenue to probe physical properties of exoplanet atmospheres and to constrain the presence of clouds and hazes. In addition, an effective surface can be imposed by refraction, thereby limiting the pressure levels probed by transmission spectroscopy. Aims. The main objective of the paper is to model the effects of refraction on photometric light curves for realistic planets and to explore the dependencies on atmospheric physical parameters. We also explore under which circumstances transmission spectra are significantly affected by refraction. Finally, we search for refraction signatures in photometric residuals in Kepler data. Methods. We use the model of Hui & Seager (2002, ApJ, 572, 540) to compute deflection angles and refraction transit light curves, allowing us to explore the parameter space of atmospheric properties. The observational search is performed by stacking large samples of transit light curves from Kepler. Results. We find that out-of-transit refraction shoulders are the most easily observable features, which can reach peak amplitudes of ~10 parts per million (ppm) for planets around Sun-like stars. More typical amplitudes are a few ppm or less for Jovians and at the sub-ppm level for super-Earths. In-transit, ingress, and egress refraction features are challenging to detect because of the short timescales and degeneracies with other transit model parameters. Interestingly, the signal-to-noise ratio of any refraction residuals for planets orbiting Sun-like hosts are expected to be similar for planets orbiting red dwarfs and ultra-cool stars. We also find that the maximum depth probed by transmission spectroscopy is not limited by refraction for weakly lensing planets, but that the incidence of refraction can vary significantly for strongly lensing planets. We find no signs of refraction features in the stacked Kepler light curves, which is in agreement with our model predictions.