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abstract: 'We report a thorough theoretical study of the low temperature phase diagram of [[Cs$_2$CuCl$_4$]{}]{}, a spatially anisotropic spin $S=1/2$ triangular lattice antiferromagnet, in a magnetic field. Our results, obtained in a quasi-one-dimensional limit in which the system is regarded as a set of weakly coupled Heisenberg chains, are in excellent agreement with experiment. The analysis reveals some surprising physics. First, we find that, when the magnetic field is oriented within the triangular layer, spins are actually most strongly correlated within planes [*perpendicular*]{} to the triangular layers. This is despite the fact that the inter-layer exchange coupling in [[Cs$_2$CuCl$_4$]{}]{} is about an order of magnitude smaller than the weakest (diagonal) exchange in the triangular planes themselves. Second, the phase diagram in such orientations is exquisitely sensitive to tiny interactions, heretofore neglected, of order a few percent or less of the largest exchange couplings. These interactions, which we describe in detail, induce entirely new phases, and a novel commensurate-incommensurate transition, the signatures of which are identified in NMR experiments. We discuss the differences between the behavior of [[Cs$_2$CuCl$_4$]{}]{} and an ideal two-dimensional triangular model, and in particular the occurrence of magnetization plateaux in the latter. These and other related results 