Optimal feedback control of densities, or distributions in general, is a topic of burgeoning interest in the systems-control community. The mathematical development provides a unified viewpoint with two different interpretations: active control of stochastic uncertainties for a single dynamical system, and shaping the population density of an ensemble of systems. The former finds application in using feedback to allow the system meet desired statistical accuracy. The latter finds application in shaping the concentration of the dynamical agents such as in swarm control, and from this perspective, can be viewed as the continuum limit of the decentralized stochastic optimal control. Recent developments have pointed out that the unifying framework, in fact, subsumes other contemporary problems of interest in physics and machine learning, such as the Schr\"{o}dinger bridge and the optimal mass transport. In this talk, we will give a brief summary of the rapid developments emerging from the control literature, and then focus on the theory and algorithms for the case when the underlying trajectory-level evolution has prior nonlinear dynamics. It will be shown that several cases of interest to the control community, such as gradient, mixed conservative-dissipative, and feedback linearizable nonlinearities, lead to tractable theory and algorithms.  We will also discuss application case studies, from power systems to automated driving, to illustrate the scope of the recent progress, and also to highlight the exciting opportunities ahead.