The need for new sources of energy is expected to become a critical problem within the next few decades. Although controlled fusion is a very challenging technology, a fusion power reactor would offer significant advantages over existing energy sources, including no air pollution or greenhouse gases, no risk of nuclear accident, no generation of material for nuclear weapons, low-level radioactive waste, and a world-wide available, nearly infinite supply of fuel, which would thus eliminate international tensions caused by imbalance in fuel supply. Tokamaks, which are the major and most promising magnetic confinement approach to fusion being pursued around the world, are high order, nonlinear systems with a large number of instabilities, so there are many extremely challenging mathematical modeling and control problems, which must be solved before a fusion power system becomes a viable entity. In this paper, we introduce briefly the basis of magnetic confinement fusion devices, and describe some of the many challenging tokamak plasma control problems, linking them with other papers presented within the special session on "Control of Fusion Plasmas in Tokamaks" at this conference.