1 Overview 2 Background 2.1 Crystalline structure and electronic dispersion 2.2 Magnetic field induced dimensional crossover 2.3 Quantum level structure 2.4 Triplet versus singlet superconductivity in a magnetic field 2.5 A minimal Hamiltonian 2.6 Theoretical upper critical field along the bt direction 2.7 Qualitative effects on non-magnetic impurities 3 Recent Experiments on (TMTSF)2PF6 3.1 Upper critical field 3.2 77Se Knight shift and nuclear-magneto-resonance measurements 3.3 Coexistence of spin density wave and superconductivity 3.4 Non-Fermi liquid behavior of the normal state 4 Recent Experiments on (TMTSF)2C104 4.1 Non-magnetic impurity effect 4.2 Upper critical field 4.3 Thermal conductivity and heat capacity 4.4 Muon and nuclear spin resonances 4.5 Non-Fermi liquid behavior of the normal state 5 Pairing Symmetry 5.1 Superconductivity in high magnetic fields 5.2 Paramagnetism of reentrant phases 5.3 Upper critical fields in singlet and triplet superconductors 5.4 Phase fluctuations and angular dependence of upper critical field 5.5 Angle-dependent heat capacity 5.6 Linear temperature dependence of nuclear spin relaxation rate 5.7 Group theory and symmetry of distinct superconducting states 6 Inhomogeneous Pairing States 6.1 Upper critical field of a singlet LOFF state 6.2 Singlet-triplet mixing in a LOFF state 6.3 Microscopic coexistence of spin density wave and sup erconductivity 7 Origins of Cooper Pairing 7.1 Phonon mediated attraction 7.2 Spin fluctuation mediated interaction 7.3 Coexistence of spin and charge fluctuations 7.4 Other pairing mechanisms 8 Tunneling Experiments and Josephson Effect 8.1 Tunneling spectroscopy and zero-bias conductance peak 8.2 Josephson effect 9 Open Questions References