Variable-speed-of-light (VSL) cosmologies are currently attracting much int
erest as a possible alternative to cosmological inflation. We discuss the f
undamental geometrodynamic aspects of VSL cosmologies, and provide several
alternative implementations. These implementations provide a large class of
VSL cosmologies that pass the zeroth-order consistency tests of being comp
atible with both classical Einstein gravity and low-energy particle physics
. While they solve the "kinematic" puzzles as well as inflation does, VSL c
osmologies typically do not solve the flatness problem since in their pures
t form no violation of the strong energy condition occurs. Nevertheless, th
ese models are easy to unify with inflation.