Our long experience with Newtonian potentials has inured us to the vie
w that gravity only produces local effects. In this paper we challenge
this quite deeply ingrained notion and explicitly identify some intri
nsically global gravitational effects. In particular we show that the
global cosmological Hubble flow can actually modify the motions of sta
rs and gas within individual galaxies, and even do so in a way which c
an apparently eliminate the need for galactic dark matter. Also we sho
w that a classical light wave acquires an observable, global, path-dep
endent phase in traversing a gravitational field. Both of these effect
s serve to underscore the intrinsic difference between nonrelativistic
and relativistic gravity.