We present results and new techniques in the art of efficient calculations of scattering amplitudes in gauge and gravity theories. In particular, the structure of amplitudes, improvements of multi-loop tools, and explicit calculations are treated. First, we explore a new structure in tree amplitudes. It is presented in the form of an identity -- analogous to the Jacobi identity for color factors -- satisfied by the kinematic factors of tree diagrams in amplitudes of massless gauge theories. It allows us to find new relations between color-ordered partial amplitudes, and to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the Kawai-Lewellen-Tye relations between gauge and gravity tree amplitudes. Later, we discuss the modern unitarity method, which enables efficient multiloop calculations in gauge and gravity theories. This tool is improved by the method of maximal cuts, in which we cut all propagators of a given integral. We illustrate the effectiveness of this new tool by computing an ansatz for the planar five-loop four-point amplitudes in N = 4 super-Yang-Mills theory. Finally, we demonstrate a tree-loop calculation pointing to the possible ultraviolet finiteness of N = 8 supergravity in four dimensions.
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