Background:In the coming decades space telescopes will be constructed that will attempt to find the gaseous products of oxygenic photosynthesis, the most promising biosignatures of life, in the atmospheres of temperate Earth-like planets orbiting distant stars. Aims: This paper aims to provide a synthesis of the range of feasible targets -either planets or their satellites -that could harbour photosynthesis. Methods: We calculated photosynthetically active radiation (PAR) fluxes on a diversity of planetary bodies including those receiving direct light from a single star, similarly to the Earth, and investigated the potential of these fluxes to support photosynthesis. Results: All main sequence stars emit radiation that is capable of supporting photosynthesis on Earth-like planets. We discuss tidally-locked M star planets as a special case. Less conventional targets for searches include large moons orbiting gas giant planets, which receive reflected light from their host planets and from the host star, planets in stable orbits in binary star systems, and the search for two planets within the same star system with photosynthetic signatures. Conclusions: A diversity of planetary bodies are targets in the search for extrasolar photosynthesis. The demonstration that many or none of these candidate planetary bodies harbour photosynthesis would be an important conclusion in understanding the evolution and prevalence of photosynthesis.