At very high temperatures and/or densities, one expects to observe a phase transition or crossover from ordinary strongly interacting matter to a plasma of quarks and gluons. A primary motivation for the construction of the Relativistic Heavy Ion Collider (RHIC) at Brookhaven National Laboratory was to observe the quark--gluon plasma and determine its properties. During the early development of the Universe matter was in the plasma state, and the quark-gluon plasma may be a central component of neutron stars today. The behavior of strongly interacting matter in the vicinity of the phase transition or crossover is inherently a strong coupling problem, which can only be studied from first principles through lattice gauge theory calculations. Among the issues that can uniquely be addressed by lattice calculations are the nature of the transition, the temperature at which it occurs, the properties of the plasma, and the equation of state. Indeed, it is the lattice that has given us the best estimates of the temperature of the deconfinement transition, approximately 175 MeV, and first measurements of the equation of state and the quark number susceptibilities. The latter are related to event by event fluctuations in heavy-ion collions. The figure at the upper right shows the energy density of strongly interacting matter as a function of temperature for zero baryon density, and that at the lower right shows several of the quark number susceptibilities. All of these quantities increase sharply as the relevant degrees of freedom change from mesons and nucleons at low temperatures to quarks at high temperatures. These results and more accurate ones anticipated from work now in progress will be crucial to the interpretation of ongoing heavy--ion experiments in the United States and Europe.