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 noncommutative quantum field theories by showing that the equation of motion considered as insertion in the generating functional Z c [j] of connected Green functions makes sense (at least at one-loop level). 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: Explicit computations are performed at one-loop order and the generalization to higher loops is commented upon. Finally, we discuss the renormalizability of various models for a self-interacting complex scalar field by using the approach of algebraic renormalization.1 It is possible to remedy this problem by considering supersymmetry, e.g. the Wess-Zumino model on Moyal space [5]. However, in the present paper we restrict our attention to non-supersymmetric models.2 In this context, we should mention the so-called twisted approach to φ 4 -theory for which there has been some recent progress (see for instance reference [8]), but which we will not discuss here.3 In the Grosse-Wulkenhaar case, the initial proof was established by its authors by using the Wilson-Polchinski renormalization group approach in a matrix base. A later proof [10] relied on multi-scale analysis.