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The memory wall challenge -- the growing disparity between CPU speed and memory speed -- has been one of the most critical and long-standing challenges in computing. For high performance computing, programming to achieve efficient execution of parallel applications often requires more tuning and optimization efforts to improve data and memory access than for managing parallelism. The situation is further complicated by the recent expansion of the memory hierarchy, which is becoming deeper and more diversified with the adoption of new memory technologies and architectures such as 3D-stacked memory, non-volatile random-access memory (NVRAM), and hybrid software and hardware caches. The authors believe it is important to elevate the notion of memory-centric programming, with relevance to the compute-centric or data-centric programming paradigms, to utilize the unprecedented and ever-elevating modern memory systems. Memory-centric programming refers to the notion and techniques of exposing hardware memory system and its hierarchy, which could include DRAM and NUMA regions, shared and private caches, scratch pad, 3-D stacked memory, non-volatile memory, and remote memory, to the programmer via portable programming abstractions and APIs. These interfaces seek to improve the dialogue between programmers and system software, and to enable compiler optimizations, runtime adaptation, and hardware reconfiguration with regard to data movement, beyond what can be achieved using existing parallel programming APIs. In this paper, we provide an overview of memory-centric programming concepts and principles for high performance computing.