Significant investigations in the area of scrape-off layer (SOL) turbu
lence theory and simulations are reviewed. The paper begins with descr
iption and derivation of the various models investigating specific lin
ear modes as well as a discussion of the regions of validity. Special
attention is given to various low-frequency electromagnetic drift-type
s modes in an x-point divertor geometry, which are generally believed
to be relevant under normal operating conditions for current and futur
e large fusion devices. The anomalous transport from simulations and f
rom mixing length estimates are discussed and compared with results in
fered from experiments. Studies of mechanisms for the L-H transition d
ue to turbulent transport in the SOL, and its impact on the II-mode po
wer threshold, are also surveyed.