Prices of goods and services in different industries can be fixed or can vary according to different criteria, such as demand, competition, discounts, profitability, etc. The concept of variable price changes is called nonlinear pricing, and is sometimes misunderstood by stakeholders or competitors. A concrete example would be frequent-flyer programmes in the airline industry which offer different prices to different people. Yet there is a whole science and logic behind price changes and discounts, such as how to keep a product profitable or how to get rid of slow stock. Disentangling the reasons behind loyalty discount schemes is essential for competition and to separate anticompetitive actions from harmless or low-impact price changes. Studying nonlinear pricing is the objective of the EU-funded project 'Nonlinear Pricing in Vertically Related Industries' (Nonlin). It aims to produce results that will help in policy-making and formulating competition laws. Generally, nonlinear discount schemes in retail markets have received much attention and are clearer than those used in relationships between manufacturers and retailers. In these sectors, nonlinear pricing typically involves discounts where higher volume purchases lead to lower prices. Some of these discounts make buyers purchase more from the firm employing the discount and less from its rivals. But these practices and discounts often come under fire by antitrust laws (laws that maintain or promote market competition by regulating anti-competitive conduct). It is usually big businesses that are involved, and antitrust laws are normally concerned when these practices threaten the economic well-being of another large competitor. Sometimes pricing policies which allow severe discounts by manufacturers pose a challenge to economic theory. This happens because it is difficult to explain why a firm would charge less for a larger order if its intentions were benign, and raises the eyebrows of antitrust law enforcers. But economic research shows that associating dominant firms' use of such discounts with foreclosure might be inappropriate. Moreover, firms commonly employ such discounts where no foreclosure concern exists. These observations and other recent developments in European and US laws underline the importance of loyalty discounts. In light of this, the project is studying the role of loyalty discounts in firms' commercial behaviour and identifying circumstances where loyalty discounts can generate efficiencies. It is now clear that there is not one answer on nonlinear pricing. It can be healthy in some cases and unhealthy in others. Once the Nonlin project completes its mandate, policy-makers will be armed with more knowledge to review and fine-tune antitrust laws in a way that benefits industry.