We review the current understanding of superconductivity in the
quasi-one-dimensional organic conductors of the Bechgaard and Fabre salt
families. We discuss the interplay between superconductivity,
antiferromagnetism, and charge-density-wave fluctuations. The connection to
recent experimental observations supporting unconventional pairing and the
possibility of a triplet-spin order parameter for the superconducting phase is
also presented.Comment: (v1) 30 pages, 13 figures; Review article for the 20th anniversary of
high-Tc superconductivity, to appear in J. Low Temp. Phys. (v2) 1 Ref. adde