With traditional computing technologies reaching their limit, a new field has emerged seeking to follow the example of the human brain into a new era: neuromorphic computing. This paper provides an introduction to neuromorphic computing, why this and other new computing systems are needed, and what technologies currently exist in the neuromorphic field. It begins with a general introduction into the history of traditional computing and its present problems, and then proceeds to a general overview of neuromorphic systems. It subsequently discusses the main technologies currently in development. For completeness, the paper first discusses neuromorphic-style computing on traditional hardware, and then discusses the two top branches of specialized hardware in this field; neuromorphic chips and photonic systems. Both branches are explained as well as their relative benefits and drawbacks. The paper concludes with a summary and an outlook on the future.