The paper contains general results on the uniqueness of a DG enhancement for
triangulated categories. As a consequence we obtain such uniqueness for the
unbounded categories of quasi-coherent sheaves, for the triangulated categories
of perfect complexes, and for the bounded derived categories of coherent
sheaves on quasi-projective schemes. If a scheme is projective then we also
prove a strong uniqueness for the triangulated category of perfect complexes
and for the bounded derived categories of coherent sheaves.