It is reported that plastic waste is accumulating in the oceans at an alarming rate. A significant proportion of this waste is plastic packaging materials, even though recycling routes and options are available to retain and reuse this oil-based resource. In addition to thermoplastic materials, fibre reinforced polymer materials are finding increased use and soon will become a concern with respect to disposal. This review presents current research and technology that aims to embrace plastics and polymer composites into a circular economy. The benefits and challenges associated with polymer recycling are highlighted, not least being the strategies required to encourage industry and society to recycle resources rather than dispose and renew.