This chapter shows the various learning methodologies that underpin the development and optimization of neuromorphic systems, which mimic the learning processes observed in biological brains. It begins by examining the conversion from Artificial Neural Networks (ANNs) to Spiking Neural Networks (SNNs). It highlights the challenges and techniques in translating continuous-valued outputs into discrete spike events, thus preserving the temporal dynamics essential for effective information processing. The chapter categorizes learning methods into supervised and unsupervised learning paradigms. In the context of supervised learning, it explores techniques such as Spike-Timing-Dependent Plasticity (STDP) and backpropagation algorithms adapted for spiking neurons, detailing how these approaches facilitate the adjustment of synaptic weights based on labeled data to improve network performance. Conversely, the chapter discusses unsupervised learning strategies. By providing a comprehensive overview of these learning techniques, the chapter emphasizes the potential of neuromorphic computing systems to tackle complex tasks in cognitive computing, robotics, and sensory processing, ultimately advancing our understanding of artificial intelligence aligned with biological principles.