  This paper first generalises the Bogomolov-Tian-Todorov unobstructedness
theorem to the case of Calabi-Yau threefolds with canonical singularities. The
deformation space of such a Calabi-Yau threefold is no longer smooth, but the
general principle is that the obstructions to deforming such a threefold are
precisely the obstructions to deforming the singularities of the threefold.
Secondly, these results are applied to smoothing singular Calabi-Yau threefolds
with crepant resolutions. Any such Calabi-Yau threefold with isolated complete
intersection singularities which are not ordinary double points is smoothable.
A Calabi-Yau threefold with non-complete intersection isolated singularities is
proved to be smoothable under much stronger hypotheses.
