Non-convex heuristics have been used to solve phase retrieval problems for decades, but only recently have convergence guarantees been obtained for some non-convex algorithms, mostly in the case where the sensing vectors are random. Algorithms for which such guarantees were established typically have a particular form: they consist in finding a good initial point, then doing a gradient descent over a well-chosen non-convex objective function, which does not encompass most algorithms actually used in applications. In this talk, I will explain how to obtain identical convergence guarantees for an algorithm closer to practice, by replacing the gradient descent with the very classic alternating projections method, and discuss the issues that arise when trying to further extend these results to the precise methods used in applications.