This chapter reviews the forces that have shaped current competition laws and initiatives, in particular those that may ease convergence and cooperation between the USA and the EU. Even if convergence is eased when countries are developed, the objectives and the means put in place to attain these objectives may differ across countries. Differences may in turn generate tensions, and therefore shape further developments of the law. Subsequently, this chapter discusses the specific case of state aid control, an EU specificity which has on the one hand helped to ensure the primacy of competition policy over industrial policy, and has prevented potential wasteful "subsidy wars" between member states. However, on the other hand, this policy has been accused at times of hurting the competitiveness of "European champions." Finally, the chapter looks at current challenges facing competition policy; focusing first on new developments as far as state aid control is concerned, namely the State Aid Action Plan, and the special case of aid to innovation. Here, the focus will be on the pros and cons of this policy, namely its potential ability to better address market failures, but also the potential risk of lax enforcement in the name of "aid to innovation." This danger might be particularly problematic in an era which has witnessed the fast rise to prominence of some emerging-economy powers (like Brazil, Russia, India and China) which do not necessarily share the competition-policy philosophy of the EU and USA. While the chapter discusses how the common ground reached by these two players could serve as the basis for a global competition policy, it also stresses the potential tensions that could arise from the assertiveness of state interests by public corporations and sovereign funds from these emerging countries.