The current environmental policy of the European Union promotes a circular economy, wherein all waste generated by human activity should be managed in the most environmentally friendly way possible. The circular economy aims to abandon the predatory exploitation of natural resources and keep resources in the economic cycle for as long as possible, significantly reducing the environmental impact of industrial activity. Waste generated in construction engineering (construction and demolition waste – C&D waste), if unavoidable, should be reused or recycled first. A suitable system for the management of C&D waste should include the proper identification of waste, source separation, and collection divided into a minimum of 6 fractions (wood, metals, glass, plastics, gypsum, mineral waste including concrete, brick, tiles, ceramic materials, and stones). The paper reviews scientific papers, the EU Construction and Demolition Waste Protocol and Guidelines, and technical solutions for waste logistics and processing, as well as quality management, which, according to the authors, are among the significant challenges in the modern world. The paper also highlights specific directions for the use of C&D materials from building construction works, as well as building renovation and demolition works. Additionally, the paper provides an expanded analysis of the limitations of legal, technical, and economic considerations.