Memory-centric computing aims to enable computation capability in and near all places where data is generated and stored. As such, it can greatly reduce the large negative performance and energy impact of data access and data movement, by fundamentally avoiding data movement and reducing data access latency & energy. Many recent studies show that memory-centric computing can greatly improve system performance and energy efficiency. Major industrial vendors and startup companies have also recently introduced memory chips that have sophisticated computation capabilities. This talk describes promising ongoing research and development efforts in memory-centric computing. We classify such efforts into two major fundamental categories: 1) processing using memory, which exploits analog operational properties of memory structures to perform massively-parallel operations in memory, and 2) processing near memory, which integrates processing capability in memory controllers, the logic layer of 3D-stacked memory technologies, or memory chips to enable high-bandwidth and low-latency memory access to near-memory logic. We show both types of architectures (and their combination) can enable orders of magnitude improvements in performance and energy consumption of many important workloads, such as graph analytics, databases, machine learning, video processing, climate modeling, genome analysis. We discuss adoption challenges for the memory-centric computing paradigm and conclude with some research & development opportunities.