Payment systems based on fixed prices have become the dominant model to finance hospitals across OECD countries. In the early 1980s, Medicare in the United States introduced the Diagnosis Related Groups (DRG) system. The idea was that hospitals should be paid a fixed price for treating a patient within a given diagnosis or treatment. The system then spread to other European countries (e.g., France, Germany, Italy, Norway, Spain, the United Kingdom) and high-income countries (e.g., Canada, Australia). The change in payment system was motivated by concerns over rapid health expenditure growth, and replaced financing arrangements based on reimbursing costs (e.g., in the United States) or fixed annual budgets (e.g., in the United Kingdom). A more recent policy development is the introduction of pay-for-performance (P4P) schemes, which, in most cases, pay directly for higher quality. This is also a form of regulated price payment but the unit of payment is a (process or outcome) measure of quality, as opposed to activity, that is admitting a patient with a given diagnosis or a treatment. Fixed price payment systems, either of the DRG type or the P4P type, affect hospital incentives to provide quality, contain costs, and treat the right patients (allocative efficiency). Quality and efficiency are ubiquitous policy goals across a range of countries. Fixed price regulation induces providers to contain costs and, under certain conditions (e.g., excess demand), offer some incentives to sustain quality. But payment systems in the health sector are complex. Since its inception, DRG systems have been continuously refined. From their initial (around) 500 tariffs, many DRG codes have been split in two or more finer ones to reflect heterogeneity in costs within each subgroup. In turn, this may give incentives to provide excessive intensive treatments or to code patients in more remunerative tariffs, a practice known as upcoding. Fixed prices also make it financially unprofitable to treat high cost patients. This is particularly problematic when patients with the highest costs have the largest benefits from treatment. Hospitals also differ systematically in costs and other dimensions, and some of these external differences are beyond their control (e.g., higher cost of living, land, or capital). Price regulation can be put in place to address such differences. The development of information technology has allowed constructing a plethora of quality indicators, mostly process measures of quality and in some cases health outcomes. These have been used both for public reporting, to help patients choose providers, but also for incentive schemes that directly pay for quality. P4P schemes are attractive but raise new issues, such as they might divert provider attention and unincentivized dimensions of quality might suffer as a result.