The behaviour of mammalian cells in a tissue is governed by the three-dimensional (3D) microenvironment and involves a dynamic interplay between biochemical and mechanical signals provided by the extracellular matrix (ECM), cell–cell interactions and soluble factors. The complexity of the microenvironment and the context-dependent cell responses that arise from these interactions have posed a major challenge to understanding the underlying regulatory mechanisms. Here we develop an experimental paradigm to dissect the role of various interacting factors by simultaneously synthesizing more than 1,000 unique microenvironments with robotic nanolitre liquid-dispensing technology and by probing their effects on cell fate. Using this novel 3D microarray platform, we assess the combined effects of matrix elasticity, proteolytic degradability and three distinct classes of signalling proteins on mouse embryonic stem cells, unveiling a comprehensive map of interactions involved in regulating self-renewal. This approach is broadly applicable to gain a systems-level understanding of multifactorial 3D cell–matrix interactions.