Making predictions about aliens is not an easy task. Most previous work has focused on extrapolating from empirical observations and mechanistic understanding of physics, chemistry and biology. Another approach is to utilize theory to make predictions that are not tied to details of Earth. Here we show how evolutionary theory can be used to make predictions about aliens. We argue that aliens will undergo natural selection – something that should not be taken for granted but that rests on firm theoretical grounds. Given aliens undergo natural selection we can say something about their evolution. In particular, we can say something about how complexity will arise in space. Complexity has increased on the Earth as a result of a handful of events, known as the major transitions in individuality. Major transitions occur when groups of individuals come together to form a new higher level of the individual, such as when single-celled organisms evolved into multicellular organisms. Both theory and empirical data suggest that extreme conditions are required for major transitions to occur. We suggest that major transitions are likely to be the route to complexity on other planets, and that we should expect them to have been favoured by similarly restrictive conditions. Thus, we can make specific predictions about the biological makeup of complex aliens.