Over the last 15–20 years there has emerged a new branch of investigations into phase retrieval in protein crystallography that focus on the use of so-called iterative projection algorithms for ab initio phasing. These investigations are somewhat distinct from existing phasing methods, and have come about from the recent availability of X-ray free-electron lasers, interest in X-ray single particle imaging, and new theoretical insights and algorithmic advances. These methods are driving a number of new and novel approaches to phasing in protein crystallography. They can reduce the experimental demands, reduce model bias and accommodate new kinds of data from new experiments. These developments, and their relationship to conventional phasing methods in protein crystallography, are outlined in this chapter.