Living tissue is able to withstand large stresses in everyday life, yet it also actively adapts to dynamic loads. This remarkable mechanical behaviour emerges from the interplay between living cells and their non-living extracellular environment. Here we review recent insights into the biophysical mechanisms involved in the reciprocal interplay between cells and the extracellular matrix and how this interplay determines tissue mechanics, with a focus on connective tissues. We first describe the roles of the main macromolecular components of the extracellular matrix in regards to tissue mechanics. We then proceed to highlight the main routes via which cells sense and respond to their biochemical and mechanical extracellular environment. Next we introduce the three main routes via which cells can modify their extracellular environment: exertion of contractile forces, secretion and deposition of matrix components, and matrix degradation. Finally we discuss how recent insights in the mechanobiology of cell-matrix interactions are furthering our understanding of the pathophysiology of connective tissue diseases and cancer, and facilitating the design of novel strategies for tissue engineering.