Video compression is a fundamental topic in the visual intelligence, bridging visual signal sensing/capturing and high-level visual analytics. The broad success of artificial intelligence (AI) technology has enriched the horizon of video compression into novel paradigms by leveraging end-to-end optimized neural models. In this survey, we first provide a comprehensive and systematic overview of recent literature on end-to-end optimized learned video coding, covering the spectrum of pioneering efforts in both uni-directional and bi-directional prediction based compression model designation. We further delve into the optimization techniques employed in learned video compression (LVC), emphasizing their technical innovations, advantages. Some standardization progress is also reported. Furthermore, we investigate the system design and hardware implementation challenges of the LVC inclusively. Finally, we present the extensive simulation results to demonstrate the superior compression performance of LVC models, addressing the question that why learned codecs and AI-based video technology would have with broad impact on future visual intelligence research.