This topical review presents an overview of the common and less common observations of rainbows in natural rainfall, and the theoretical concepts that have been developed for their explanation. Mainly throughout the last 20 years, many new and intriguing effects have been photographed or documented for the first time, such as higher-order (tertiary, quaternary, etc) and twinned rainbows, as well as rainbows generated by nearby artificial light sources. In order to provide a sound explanation, the inclusion of natural non-spherical (i.e. oblate) raindrop shapes as well as natural broad polydisperse raindrop distributions into the classical rainbow theory (Lorenz–Mie and Debye scattering) is outlined. Thus, the article provides a condensed up-to-date synopsis complementing classical textbooks and earlier reviews on the physics of rainbows. It is intended to serve both active sky observers as well as physics teachers who want to keep up with current developments in the field.