  A review is made of recent efforts to add a gravitational field to
noncommutative models of space-time. Special emphasis is placed on the case
which could be considered as the noncommutative analog of a parallelizable
space-time. It is argued that, at least in this case, there is a rigid relation
between the noncommutative structure of the space-time on the one hand and the
nature of the gravitational field which remains as a `shadow' in the
commutative limit on the other.
