The chapter thoroughly investigates neuromorphic engineering, providing readers with a solid foundation. It opens with an introduction that establishes the basic principles of neuromorphic computing and underscores its importance in modern technology. The neuromorphic systems design challenges section addresses technical and conceptual hurdles in creating effective and scalable neuromorphic systems, emphasizing the intricacies involved in their development. Next, Neural Network Models are explored in depth, shedding light on the various architectures that emulate brain-like functions and their respective roles. The chapter also presents Learning in Spiking Neural Networks and synapse memory technologies, focusing on innovative learning algorithms and memory technologies that enhance the system’s adaptability and performance. These discussions are enriched with examples and case studies that illustrate practical applications. Concluding with Exercises, the chapter offers practical tasks designed to reinforce the concepts covered, allowing readers to apply their knowledge and gain a deeper understanding of neuromorphic computing principles and their applications. This comprehensive approach ensures that readers are well-equipped to navigate and contribute to the evolving field of neuromorphic engineering.