  We develop techniques for computing and analyzing multiple unitarity cuts of
Feynman integrals, and reconstructing the integral from these cuts. We study
the relations among unitarity cuts of a Feynman integral computed via
diagrammatic cutting rules, the discontinuity across the corresponding branch
cut, and the coproduct of the integral. For single unitarity cuts, these
relations are familiar. Here we show that they can be generalized to sequences
of unitarity cuts in different channels. Using concrete one- and two-loop
scalar integral examples we demonstrate that it is possible to reconstruct a
Feynman integral from either single or double unitarity cuts. Our results offer
insight into the analytic structure of Feynman integrals as well as a new
approach to computing them.
