There is a growing interest in the constrained Newsvendor problem. This interest has generated several methods and approaches to solving it. These methods and approaches vary in nature and outcomes ranging from iterative to approximate and those which can tackle one constraint to other that can deal with multiple ones. In this paper, these existing methods and approaches are reviewed and their performance are compared. The comparisons include, inter alia, the number of constraints which can be handled by each, the considered probability density functions (PDFs.), the complexity and ease of applying these methods and the closeness to the optimal solution. Examples are given to illustrate the advantage of the compared methods and approaches in terms of the different performance measures.