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.

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