The role of soluble messengers in directing cellular behaviours has been recognized for decades. However, many cellular processes, including adhesion, migration and stem cell differentiation, are also governed by chemical and physical interactions with non-soluble components of the extracellular matrix (ECM). Among other effects, a cell's perception of nanoscale features such as substrate topography and ligand presentation, and its ability to deform the matrix via the generation of cytoskeletal tension play fundamental roles in these cellular processes. As a result, many biomaterials-based tissue engineering and regenerative medicine strategies aim to harness the cell's perception of substrate stiffness and nanoscale features to direct particular behaviours. However, since cell-ECM interactions vary considerably between two-dimensional (2-D) and three-dimensional (3-D) models, understanding their influence over normal and pathological cell responses in 3-D systems that better mimic the in vivo microenvironment is essential to translate such insights efficiently into medical therapies. This review summarizes the key findings in these areas and discusses how insights from 2-D biomaterials are being used to examine cellular behaviours in more complex 3-D hydrogel systems, in which not only matrix stiffness, but also degradability, plays an important role, and in which defining the nanoscale ligand presentation presents an additional challenge.