Four hundred years ago, Hugo Grotius defined the notion of Mare Liberum, leading to the concept of the 'Freedom of the Seas'. This concept has dominated humanity's relationship with the oceans and its renewable resources ever since. We present the conceptual reasons for society having arrived at the current ecological, economic and policy dilemma of widespread overfishing by global marine fisheries. We propose a call for global action to change our attitudes and behaviour towards the oceans away from 'free and open' towards 'heritage'. We then propose one mechanism (ocean zoning) that we consider crucial to address what is clearly a supra-national problem of global dimensions.