  We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the
anisotropic triangular lattice in the large-N limit. These two models may
describe respectively the magnetic and electronic properties of the family of
layered organic materials $\kappa$-(BEDT-TTF)$_2$X. The Heisenberg model is
also relevant to the frustrated antiferromagnet, Cs$_2$CuCl$_4$. We find rich
phase diagrams for each model. The Sp(N) antiferromagnet is shown to have five
different phases as a function of the size of the spin and the degree of
anisotropy of the triangular lattice. The effects of fluctuations at finite-N
are also discussed. For parameters relevant to Cs$_2$CuCl$_4$ the ground state
either exhibits incommensurate spin order, or is in a quantum disordered phase
with deconfined spin-1/2 excitations and topological order. The SU(N)
Hubbard-Heisenberg model exhibits an insulating dimer phase, an insulating box
phase, a semi-metallic staggered flux phase (SFP), and a metallic uniform
phase. The uniform and SFP phases exhibit a pseudogap. A metal-insulator
transition occurs at intermediate values of the interaction strength.
