P2P has become a major part of Internet traffic. Along with a growing economic e-commerce activity in which consumers purchase music, video, software and books over the Internet, P2P file sharing networks have enabled a free widespread public access to copyrighted material. A long lasting conflict accompanied by an impressive ``arms race'' has been developing between ``producers'' (i.e. copyright owner companies) and ``users'' (part of the web surfers community). In their effort to decrease internet ``piracy'', companies have lobbied for legislation that would ban this practice and that would increase their control and monitoring on the content transferred over the Internet. They have taken legal action against companies and individuals involved in P2P developments, sued individual web surfers, have formed alliances with some service providers to prevent access to P2P networks, and sued others that were not cooperative. Our paper describes and analyzes different facets of this conflict, and the way legal actions and network technology interact. We summarize the role of other actors involved and describe other business models for the producers that can co-exist with today's P2P networks. We then introduce mathematical models that study the efficiency of measures to restrict ``piracy''.