  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.
