Using multi-terminal networks we build general methods for
constructing graphs without nowhere-zero group- and integer-valued
flows.  In this way we unify known constructions of snarks
(nontrivial cubic graphs without $3$-edge-colorings, or
equivalently, without nowhere-zero $4$-flows) and provide new ones
in the same process.  Our methods also imply new results about
nowhere-zero flows in graphs.  For example we can show that the 3-
and 5-flow conjectures of Tutte are equivalent to seemingly weaker
problems.
