In the European Union, competition law has expanded and matured, assuming a key role in the promotion of consumer welfare, economic progress and public interest in general. Nevertheless, several issues remain open. Should the European Union remain faithful to antitrust public enforcement or fully consider the complementary role of private enforcement? Are the European solutions concerning exclusionary abuses coherent and predictable? What role should National Competition Authorities play in the context of State Aid? This book attempts to analyse and discuss some open, selective questions concerning three particular topics on competition law that are becoming highly relevant in the European and national praxis: antitrust private enforcement, exclusionary abuses and state aid. To address these issues, two seminars and international conferences, supported by the European Commission, took place at Catolica Porto School of Law, Catholic University of Portugal, in March 2014 and March 2015. This publication includes the papers presented in those events, which gathered well-known and respected scholars and practitioners in the field of competition law, leading to a productive debate about EU competition law challenges in the next decade.