  CsCuCl_3 is a ferromagnetically stacked triangular spin-1/2 antiferromagnet.
We discuss models for its zero-temperature magnetization process. The models
range from three antiferromagnetically coupled ferromagnetic chains to the full
three-dimensional situation. The situation with spin-1/2 is treated by
expansions around the Ising limit and exact diagonalization. Further,
weak-coupling perturbation theory is used mainly for three coupled chains which
are also investigated numerically using the density-matrix renormalization
group technique. We find that already the three-chain model gives rise to the
plateau-like feature at one third of the saturation magnetization which is
observed in magnetization experiments on CsCuCl_3 for a magnetic field
perpendicular to the crystal axis. For a magnetic field parallel to the crystal
axis, a jump is observed in the experimental magnetization curve in the region
of again about one third of the saturation magnetization. In contrast to
earlier spinwave computations, we do not find any evidence for such a jump with
the model in the appropriate parameter region.
