  We present a variational study of the Heisenberg antiferromagnet on the
spatially anisotropic triangular lattice in magnetic field. First we construct
a simple yet accurate wavefunction for the 1/3-magnetization plateau uud phase
on the isotropic lattice. Beginning with this state, we obtain natural
extensions to nearby commensurate coplanar phases on either side of the
plateau. The latter occur also for low lattice anisotropy, while the uud state
extends to much larger anisotropy. Far away from the 1/3 plateau and for
significant anisotropy, incommensurate states have better energetics, and we
address competition between coplanar and non-coplanar states in the high field
regime. For very strong anisotropy, our study is dominated by quasi-1d physics.
The variational study is supplemented by exact diagonalization calculations
which provide a reference for testing the energetics of our trial wavefunctions
as well as helping to identify candidate phases.
