Studies of the formation of cosmic structure are entering a period of dramatic improvements in sophistication and verisimilitude. A wealth of observational data is becoming available, ranging from studies of galaxies, clusters and their cosmic distribution, to the high redshift universe and observations of microwave background fluctuations. These observations, together with enormous improvements in the scale and quality of the numerical computations that can be undertaken, promise very substantial progress in our understanding of the formation and evolution of cosmic structure.Numerical simulations are the crucial theoretical probe of non-linear gravitational and hydrodynamic cosmic evolution. The talk briefly reviews the current state of numerical structure formation studies and discusses the developments in techniques which, when coupled with current supercomputers, are leading to studies of unprecedented scope and resolution. The talk concludes with comments on future directions for structure formation studies and on the challenges inherent in simulations of increasing size. Initial results from some of the first billion particle simulations are presented.
