This article provides an overview of model predictive control (MPC) frameworks for dynamic operation of nonlinear constrained systems. Dynamic operation is often an integral part of the control objective, ranging from tracking of reference signals to the general economic operation of a plant under online changing time-varying operating conditions. We focus on the particular challenges that arise when dealing with such more general control goals and present methods that have emerged in the literature to address these issues. The goal of this article is to present an overview of the state-of-the-art techniques, providing a diverse toolkit to apply and further develop MPC formulations that can handle the challenges intrinsic to dynamic operation. We also critically assess the applicability of the different research directions, discussing limitations and opportunities for further research.