  We study the semiclassical propagation of coherent states in $d$ dimensions,
which in general involves complex classical dynamics. Several simple
approximations are derived that depend only on real classical trajectories,
among them the thawed Gaussian approximation (TGA). Apart from the TGA, all
other possibilities are able to reproduce interference and tunnelling effects,
and involve propagating a set of classical initial conditions compatible with
the quantum uncertainties. The accuracy of the results is verified in two
dimensions for the scattering by an attractive potential, for a bound nonlinear
system, for motion inside a circular billiard and for a system involving
tunnelling.
