  Graphical functions are special position space Feynman integrals, which can
be used to calculate Feynman periods and one- or two-scale processes at high
loop orders. With graphical functions, renormalization constants have been
calculated to loop orders seven and eight in four-dimensional $\phi^4$ theory
and to order five in six-dimensional $\phi^3$ theory. In this article we
present the theory of graphical functions in even dimensions $\geq4$ with
detailed reviews of known properties and full proofs whenever possible.
