  This paper addresses three topics concerning the quantization of
non-commutative field theories (as defined in terms of the Moyal star product
involving a constant tensor describing the non-commutativity of coordinates in
Euclidean space). To start with, we discuss the Quantum Action Principle and
provide evidence for its validity for non-commutative quantum field theories by
showing that the equation of motion considered as insertion in the generating
functional Zc[j] of connected Green functions makes sense. Second, we consider
the generalization of the BPHZ renormalization scheme to non-commutative field
theories and apply it to the case of a self-interacting real scalar field.
Finally, we discuss the renormalizability of various models for a
self-interacting complex scalar field by using the approach of algebraic
renormalization.
