The search for life elsewhere in the universe is one of the central aims of science in the 21st century. While most of this work is aimed at planets orbiting other stars, the search for life in our own Solar System is an important part of this endeavour. Venus is often thought to have too harsh an environment for life, but it may have been a more hospitable place in the distant past. If life evolved there in the past then the cloud decks of Venus are the only remaining niche where life as we know it might survive today. The discovery of the molecule phosphine, PH3, in these clouds has reinvigorated research looking into the possibility of life in the clouds. In this review we examine the background to studies of the possibility of life on Venus, discuss the discovery of phosphine, review conflicting and confirming observations and analyses, and then look forward to future observations and space missions that will hopefully provide definitive answers as to the origin of phosphine on Venus and to the question of whether life might exist there.