Advances in integrated circuitry from the 1950s to the present day have enabled a revolution in technology across the world. However, fundamental limits of circuitry make further improvements through historically successful methods increasingly challenging. It is becoming clear that to address new challenges and applications, new methods of computation will be required. One promising field is neuromorphic engineering, a broad field which applies biologically inspired principles to create alternative computational architectures and methods. In this work, we address why neuromorphic engineering is one of the most promising fields within emerging computational technology, detail its common principles and models, and summarize its current state and future challenges.