This paper aims to summarize, propose, and discuss existing or emerging strategies to shift towards a circular economy of materials. To clarify the landscape of existing circular practices, a new spectrum is proposed, from product-based strategies, where entire products go through several life cycles without being reprocessed, to material-based approaches, extracting, recycling, and reprocessing materials from the waste flow. As refillable packaging does not lose any functionality or value, when re-used through many life cycles, product-based strategies are globally extremely efficient and must be promoted. It appears however that their implementation is only possible at the scale of individual products such as packaging containers, relying on the cooperation of involved companies and consumers. It appears more and more urgent to focus as well on a more systematic and flexible material-oriented scheme. The example of circular glass recycling is a success in many countries, and technologies become nowadays available to extend such practices to many other materials, such as rigid plastics. An ideal would be to aim at an economy of materials that would imitate the continuous material cycle of the biosphere. Technological and business strategies are presented and discussed, aiming at a relevant impact on circularity.