As aerial robots are tasked to navigate environments of increased complexity, embedding collision tolerance in their design becomes important. In this survey we review the current state-of-the-art within the niche field of collision-tolerant micro aerial vehicles and present different design approaches identified in the literature, as well as methods that have focused on autonomy functionalities that exploit collision resilience. Subsequently, we discuss the relevance to biological systems and provide our view on key directions of future fruitful research.