The paper by M. P. Bendsøe and O. Sigmund explores the use of material interpolation schemes in topology optimization, particularly focusing on the parametrization of geometry through a grey-scale density-like interpolation function. The authors analyze and compare various approaches to this concept, considering variational bounds on effective properties of composite materials. This analysis leads to necessary conditions for the realization of grey-scale designs via composites, providing a physical interpretation of feasible and optimal designs. The paper discusses single material and multi-material structural design in elasticity and multi-physics problems, highlighting that the artificial interpolation model often aligns with microstructurally based models. Key topics include the existence of solutions, solution methods, and the role of physical models for 'grey' materials. The authors also discuss relaxation techniques, which allow for the inclusion of microstructures and composite materials in the design, and the challenges and benefits of these approaches. The paper aims to provide a comprehensive understanding of the nature of computational measures and the physical relevance of intermediate steps in topology optimization.The paper by M. P. Bendsøe and O. Sigmund explores the use of material interpolation schemes in topology optimization, particularly focusing on the parametrization of geometry through a grey-scale density-like interpolation function. The authors analyze and compare various approaches to this concept, considering variational bounds on effective properties of composite materials. This analysis leads to necessary conditions for the realization of grey-scale designs via composites, providing a physical interpretation of feasible and optimal designs. The paper discusses single material and multi-material structural design in elasticity and multi-physics problems, highlighting that the artificial interpolation model often aligns with microstructurally based models. Key topics include the existence of solutions, solution methods, and the role of physical models for 'grey' materials. The authors also discuss relaxation techniques, which allow for the inclusion of microstructures and composite materials in the design, and the challenges and benefits of these approaches. The paper aims to provide a comprehensive understanding of the nature of computational measures and the physical relevance of intermediate steps in topology optimization.