The local energy market (LEM) is emerging as a novel market mechanism to balance supply and demand as more distributed energy resources (DERs) and flexible loads integrate with power systems. LEM primarily focuses on energy transactions within distribution systems, which are closely linked to human behaviors and social activities and can extend to multi-energy carrier systems. Additionally, artificial intelligence (AI) advancements facilitate more automatic and intelligent participation in various LEMs. Consequently, LEM can pave the way to the cyber-physical-society system and price signal-defined open-access energy facilities. This chapter comprehensively reviews the conceptual development of LEM in power distribution systems, encompassing its fundamental features, structure, key implementation techniques, and transactive control methodology. Furthermore, the integration of LEM with the cyber-physical-society system and AI, multi-energy carriers, and social and human impacts is discussed.