  The role of quantum universal enveloping algebras of symmetries in
constructing a noncommutative geometry of space-time and corresponding field
theory is discussed. It is shown that in the framework of the twist theory of
quantum groups, the noncommutative (super) space-time defined by coordinates
with Heisenberg commutation relations, is (super) Poincar\'e invariant, as well
as the corresponding field theory. Noncommutative parameters of global
transformations are introduced.
