  Superconductivity in the Bechgaard salts series of quasi-one-dimensional
organic conductors occurs on the verge of spin-density-wave ordering when
hydrostatic pressure is applied. The sequence of instabilities is intimately
connected to normal state anomalies in various quantities like the temperature
dependence of electrical transport and nuclear spin-lattice relaxation rate. We
discuss how such a connection takes its origin in the interference between the
different pairing mechanisms responsible for antiferromagnetism and
superconductivity, a duo that can be comprehended in terms of a weak coupling
renormalization group theory. The recent developments along this line of though
are presented in relation to experiments.
