  We take a major step towards computing $D$-dimensional one-loop amplitudes in
general gauge theories, compatible with the principles of unitarity and the
color-kinematics duality. For $n$-point amplitudes with either supersymmetry
multiplets or generic non-supersymmetric matter in the loop, simple
all-multiplicity expressions are obtained for the maximal cuts of kinematic
numerators of $n$-gon diagrams. At $n=6,7$ points with maximal supersymmetry,
we extend the cubic-diagram numerators to encode all contact terms, and thus
solve the long-standing problem of \emph{simultaneously} realizing the
following properties: color-kinematics duality, manifest locality, optimal
power counting of loop momenta, quadratic rather than linearized Feynman
propagators, compatibility with double copy as well as all graph symmetries.
Color-kinematics dual representations with similar properties are presented in
the half-maximally supersymmetric case at $n=4,5$ points. The resulting
gauge-theory integrands and their supergravity counterparts obtained from the
double copy are checked to reproduce the expected ultraviolet divergences.
