Superconductivity which is observed in the series of quasi-one-dimensional organic conductors (TMTSF)2X is characterized by experimental features which can be related to the strong anisotropy of the band structure of these materials. We shall emphasize the interplay between magnetically ordered and superconducting ground states and the existence of a field-dependent depression of the density of states at the Fermi level below 30 K or so. Finally, we point out briefly that the quasi mean-field behavior of the superconducting transition at 1.2 K in (TMTSF)2ClO4 can be easily reconciled with a broad one-dimensional fluctuation regime within the framework of a quasi-one-dimensional theory which takes into account the quantum phase fluctuations of the order parameter and a band structure anisotropy not larger than 10.