Due to the amount of data involved in emerging deep learning and big data applications, operations related to data movement have quickly become a bottleneck. Data-centric computing (DCC), as enabled by processing-in-memory (PIM) and near-memory processing (NMP) paradigms, aims to accelerate these types of applications by moving the computation closer to the data. Over the past few years, researchers have proposed various memory architectures that enable DCC systems, such as logic layers in 3D-stacked memories or charge-sharing-based bitwise operations in dynamic random-access memory (DRAM). However, application-specific memory access patterns, power and thermal concerns, memory technology limitations, and inconsistent performance gains complicate the offloading of computation in DCC systems. Therefore, designing intelligent resource management techniques for computation offloading is vital for leveraging the potential offered by this new paradigm. In this article, we survey the major trends in managing PIM and NMP-based DCC systems and provide a review of the landscape of resource management techniques employed by system designers for such systems. Additionally, we discuss the future challenges and opportunities in DCC management.