To design a neuromorphic hardware system, it is essential to develop artificial neurons that replicate the behavior of biological neurons, together with artificial synapses that emulate the function of biological synapses. This chapter thoroughly examines crucial memory technologies for developing neuromorphic computing systems. Beginning with an overview of general memory technology, the chapter provides the specific applications and requirements of memory for neuromorphic systems. Then, it explores various memory types, including static RAM (SRAM) synapse memory and non-volatile synapse memory, emphasizing their roles and performance characteristics. The chapter also discusses Non Volatile Memory (NVM) in-memory computing, highlighting its potential to revolutionize the efficiency and functionality of neuromorphic hardware. In addition, it investigates how learning can be integrated with these advanced memory technologies to enhance system capabilities. The chapter concludes with exercises designed to apply and reinforce the discussed concepts to consolidate understanding.