Attempts to formulate supersymmetric field theories on discrete spacetime lattices have a long history. However, until recently most of these efforts have failed. In this talk I will review some of the new ideas that have finally allowed a solution to this problem for certain supersymmetric theories. I will focus my attention, in particular, on N=4 super Yang-Mills which forms one of the pillars of the AdSCFT correspondence connecting gravitational theories in anti-deSitter space to gauge theories living on the boundary. It is also integral to the scattering amplitudes program and is under intensive study using conformal bootstrap techniques. I will review the theoretical construction of the model and describe what is known analytically about the lattice theory. Following on from this I will present preliminary results stemming from the first large scale lattice study of N=4 Yang-Mills.