The concept of a circular economy has become a significant school of thought in sustainable economics over the last 10 years. This paper critically analyses the key principles underpinning the concept of the circular economy, specifically examining the thermodynamic and ecological foundations upon which these principles are apparently rooted. We examine issues related to recycling, biological and technical nutrients, restoration, energy use, elimination of waste, eco-efficiency, product lifetime and economic growth under three headings: the pyramid of waste, short cycles and eco-inefficiency. We reflect on how the economy of nature is based on an open system, not a closed system, that nature operates using short cycles, not extended lifetimes, that nature is sub-optimal, not optimal and that nature is eco-inefficient, not eco-efficient. Findings are then discussed, and we explore what we can learn from the natural world in terms of sustainability.