  We review the interplay of frustration and strong electronic correlations in
quasi-two-dimensional organic charge transfer salts, such as k-(BEDT-TTF)_2X
and Et_nMe_{4-n}Pn[Pd(dmit)2]2. These two forces drive a range of exotic phases
including spin liquids, valence bond crystals, pseudogapped metals, and
unconventional superconductivity. Of particular interest is that in several
materials there is a direct transition as a function of pressure from a spin
liquid Mott insulating state to a superconducting state. Experiments on these
materials raise a number of profound questions about the quantum behaviour of
frustrated systems, particularly the intimate connection between spin liquids
and superconductivity. Insights into these questions have come from a wide
range of theoretical techniques including first principles electronic
structure, quantum many-body theory and quantum field theory. In this review we
introduce the basic ideas of the field by discussing a simple frustrated
Heisenberg model with four spins. We then describe the key experimental
results, emphasizing that for two materials, k-(BEDT-TTF)_2Cu_2(CN)_3 and
EtMe_3Sb[Pd(dmit)_2]_2, there is strong evidence for a spin liquid ground
state, and for EtMe_3P[Pd(dmit)_2]_2, a valence bond solid ground state. We
review theoretical attempts to explain these phenomena, arguing that this can
be captured by a Hubbard model on the anisotropic triangular lattice at half
filling, and that resonating valence bond wavefunctions can capture most of the
essential physics. We review evidence that this model can have a spin liquid
ground state for a range of parameters that are realistic for the relevant
materials. We conclude by summarising the progress made thus far and
identifying some of the key questions still to be answered.
