  This is an exposition of joint work with S. Doplicher, K. Fredenhagen, and G.
Piacitelli on field theory on the noncommutative Minkowski space. The limit of
coinciding points is modified compared to ordinary field theory in a suitable
way which allows for the definition of so-called regularized field monomials as
interaction terms. Employing these in the Hamiltonian formalism results in an
ultraviolet finite S-matrix.
