The possible use of tokamaks for thermonuclear power plants is discussed, in particular tokamaks with low aspect ratio and copper toroidal field coils. Three approaches are presented. First, the existing literature is reviewed and summarized. Second, using simple analytic estimates, the size of the smallest tokamak to produce an ignited plasma is derived. This steady state energy balance analysis is then extended to determine the smallest tokamak power plant, by including the power required to drive the toroidal field and by considering two extremes of plasma current drive efficiency. Third, the analytic results are augmented by a numerical calculation that permits arbitrary plasma current drive efficiency and different confinement scaling relationships. Throughout, the importance of various restrictions is emphasized, in particular plasma current drive efficiency, plasma confinement, plasma safety factor, plasma elongation, plasma beta, neutron wall loading, blanket availability and recirculation of electric power. The latest published reactor studies show little advantage in using low aspect ratios to obtain a more compact device (and a low cost of electricity) unless either remarkably high efficiency plasma current drive and low safety factor are combined, or unless confinement (the H factor), the permissible elongation and the permissible neutron wall loading increase as the aspect ratio is reduced. These results are reproduced with the analytic model