A three-part overview of recent reformulations and symmetries of amplitudes in N=4 Super-Yang-Mills theory. \\ \\ 1. Tree-level superamplitudes, recursion relations, dual superconformal and Yangian symmetry. \\ 2. Twistor geometry, tree-level amplitudes in twistor space. Link representations. \\ 3. Loop amplitudes: integral structures and applications of generalized unitarity. Symmetries of one-loop superamplitudes.