AbstractMost major discoveries in astronomy are unplanned, and result from surveying the Universe in a new way, rather than by testing a hypothesis or conducting an investigation with planned outcomes. For example, of the ten greatest discoveries made by the Hubble Space Telescope, only one was listed in its key science goals. So a telescope that merely achieves its stated science goals is not achieving its potential scientific productivity.Several next-generation astronomical survey telescopes are currently being designed and constructed that will significantly expand the volume of observational parameter space, and should in principle discover unexpected new phenomena and new types of object. However, the complexity of the telescopes and the large data volumes mean that these discoveries are unlikely to be found by chance. Therefore, it is necessary to plan explicitly for unexpected discoveries in the design and construction. Two types of discovery are recognised: unexpected objects and unexpected phenomena.This paper argues that next-generation astronomical surveys require an explicit process for detecting the unexpected, and proposes an implementation of this process. This implementation addresses both types of discovery, and relies heavily on machine-learning techniques, and also on theory-based simulations that encapsulate our current understanding of the Universe.