In a successful tissue engineering or regenerative medicine (TRM) paradigm, a biomaterial operates as a scaffold for active cell recruitment, maintenance of adequate mechanical support and release of biochemical signals and cues that modulate cell behaviour. The extracellular matrix (ECM) is nature’s template of a biological biomaterial and is composed of proteoglycans and adhesive glycoproteins (fibronectin, laminin, collagen, elastin) that provide biochemical and physical cues to cells, thereby regulating their function, phenotype, migration and activity in development and during homeostasis. Over more than 50 years, biomedical research on ECMs has evolved from coating cell cultures with purified ECMs to engineering decellularised organ-scale tissue to design biomaterials biomimetic of the ECM composition, dynamics and structure. In this Review, we discuss the relevance of matrix properties and functions in the context of tissue regeneration and engineering; we consider proteomics (mass spectrometry-based technologies) as a valid strategy to investigate matrix features at the organic and inorganic levels; we discuss engineering approaches to design matrix-mimicry biomaterials to develop tissue-specific biomaterials for clinical application; we discuss the use of decellularisation as the most straightforward route to preserve the tissue-specific composition and ultrastructure (ECM) to develop biomaterials for clinical use; we expose challenges and opportunities of ECM-based biomaterials in the design of organotypic disease models and ex vivo production of engineered tissues; and the clinical translation strategies of functional TRM for regenerative medicine applications.