Recent years have witnessed a wave of research activities in systems science and engineering toward the control of population systems. The driving force behind this shift was geared by numerous emerging and ever-changing technologies from neuroscience, biology, and quantum physics to robotics, where many control-enabled applications involve manipulating a large ensemble of structurally identical dynamic units or agents. Owing to the large scale and complexity of ensemble systems, placing sensors or installing the infrastructure to acquire measurements of individual agents in the population is impractical at best and often impossible. Although measurements from individual agents may be unavailable, the ensemble system can be coarsely monitored at a population level, e.g., through aggregated measurements such as partial snapshots or fragmented images. In this talk, we will introduce a moment-based framework that utilizes the idea of statistical moments induced by aggregated measurements to synthesize a novel approach to controlling an ensemble system through its associated moment system. In particular, we present the connection between the ensemble control problem and the classical moment problem, by which the control-theoretic analysis, e.g., controllability, and design  can be carried over through the study of the moment system. Moreover, we will illustrate how the proposed moment-based method enables a pure data-driven architecture to infer ensemble systems with unknown dynamics and close the loop and design feedback laws for ensemble control systems.