This chapter provides a comprehensive overview of the field of neuromorphic systems, tracing its evolution from inception to its current state. The chapter begins with an introduction that outlines the motivations and goals driving neuromorphic computing. It shows the historical progression and milestones of neuromorphic engineering, highlighting key developments and influential research. The chapter is divided into three main sections, each focusing on different approaches to neuromorphic system implementation. The first section examines the software emulation approach, explicitly discussing the SpiNNaker project, which simulates spiking neural networks on a large scale. The second section explores digital hardware design approaches, featuring examples such as IBM’s TrueNorth and Intel’s Loihi, which represent significant advancements in digital neuromorphic computing. The final section covers analog and mixed-signal hardware approaches, with a detailed look at NeuroGrid, an innovative platform that integrates analog circuits to mimic neuronal behavior. This chapter compares and contrasts these varied approaches and identifies their strengths and limitations, thoroughly understanding neuromorphic systems’ current landscape and future directions.