the “ideal” model of an isolated spatially anisotropic triangular Heisenberg antiferromagnet, often presumed to apply to [[Cs$_2$CuCl$_4$]{}]{}. It clearly disagrees with experimental results for all three field orientations, as already pointed out in Ref. . In Sec. \[sec:field-along-axis\], we successfully apply the standard model to the case with a magnetic field applied perpendicular to the triangular plane, the DM interaction $D$ playing a crucial role in reconciling the behavior with experiment. Next, in Sec. \[sec:field-along-b\], we study the case of magnetic field along the $b$ (chain) axis. The $D$ term becomes rapidly negligible in this orientation, and we argue instead that the inter-plane coupling $J''$ becomes dominant. A subtle hierarchy of energy scales (see Fig. \[fig:energyscales\]) is exposed, which leads to the establishment of competing antiferromagnetic and cone phases in this case. Then, in Sec. \[sec:field-along-c\], we consider the field along the final principal axis, $c$, where an additional symmetry-allowed DM coupling plays a key role. It leads to the new incommensurate phase and an interesting commensurate-incommensurate phase transition. Having established all the ground state phases, we discuss some experimental consequences in Sec. \[sec:exper-cons\]. We give the explicit spin structures, describe the NMR lineshapes, which provide a telling confirmation of 