Continuous bioreactors are critical unit operations in a wide variety of biotechnological processes. While they can be viewed as chemical reactors, bioreactors offer unique modeling and control challenges due to the complexity of the underlying biochemical reactions and the distributed properties of the cell population. The dynamic behavior of continuous bioreactors can be strongly affected by variations between individual cells that are captured only with cell population models. The objective of this paper is to outline recent progress in dynamic analysis and feedback control of continuous bioreactors described by cell population models. The industrially important process of continuous yeast production is used to illustrate various concepts. Future research problems in cell population modeling, dynamics and control are outlined to provide insights on the key challenges and opportunities in this emerging area.