A review is presented of recent developments in the theory of fluctuat
ions in tokamak scrape-off layers. A brief summary of typical experime
ntal features is presented, followed by derivation of a flute-mode dis
persion relation including conducting-wall, curvature, axial E x B she
ar and radial compression drives. Non-linear results are reviewed, inc
luding arguments for and evidence of inverse cascading, penetration of
SOL-generated turbulence into the closed-flux-surface edge plasma, an
d large-amplitude fluid excursions, comparable to observed SOL widths.
Effects of divertor and limiter geometry, including x-point effects,
are discussed. The potential importance of atomic physics drives for r
adiative and gas-target divertors is noted, as is the possibility that
SOL turbulence originates in the core plasma. Consequences of SOL tur
bulence, including broadening of the SOL and dissipating parallel mome
ntum (of potential importance for gas-target divertors) are outlined,
and the possibility of actively exciting turbulence to achieve these o
bjectives is discussed.