We introduce the Wilson loop/amplitude duality, which states that certain gluon amplitudes in N=4 SYM are equivalent to light-like polygonal Wilson loops. We will illustrate the duality's power by computing the one loop Wilson loop analytically (matching with the known amplitudes) and then the two loop Wilson loop numerically for any number of edges. If the duality continues to hold we can thus compute two loop MHV amplitudes for any number of incoming particles. In the second part of the talk we discuss the recently conjectured new symmetry dual superconformal symmetry of the complete S-matrix of N=4 SYM. We prove its presence at tree-level and find new constraints it puts on the one loop amplitude.