Theory and observations of river plumes are reviewed. The importance o
f the Kelvin number in characterizing anticipated plume behavior is st
ressed. In the absence of strong external forcing, a northern hemisphe
re plume will turn anticyclonically and attach to the coast, where it
then merges into a coastal current. Observations and theory of such co
astal currents are also reviewed, with emphasis on flaws over shallow
continental shelves. Major unresolved questions involve the processes
controlling mixing of coastal current waters with ambient shelf waters
and the dynamics of the plume in the region where it attaches to the
coast.