The judgment that a given event is epistemically improbable is necessary but insufficient for us to conclude that the event is surprising. Paul Horwich has argued that surprising events are, in addition, more probable given alternative background assumptions that are not themselves extremely improbable. I argue that Horwich's definition fails to capture important features of surprises and offer an alternative definition that accords better with intuition. An important application of Horwich's analysis has arisen in discussions of fine-tuning arguments. In the second part of the paper I consider the implications for this argument of employing my definition of surprise. I argue that advocates of fine-tuning arguments are not justified in attaching significance to the fact that we are surprised by examples of fine-tuning.