The scattering amplitudes of N=4 super-Yang-Mills theory exhibit many remarkable hidden symmetries and structures. After giving a brief introduction to N=4 super-Yang-Mills theory, I will describe a new form of hidden simplicity in the amplitudes, notably that the loop integrands can be expressed in dlog form. I will explain how this form arises from computing the scattering amplitudes using a Wilson loop in twistor space and describe a systematic method for evaluating such integrals.
