This Perspective addresses the design, creation, characterization and control of synthetic quantum materials with strong electronic correlations. We show how emerging synergies between theoretical/computational approaches and materials design/experimental probes are driving recent advances in the discovery, understanding and control of new electronic behaviour in materials systems with interesting and potentially technologically important properties. The focus here is on transition metal oxides, where electronic correlations lead to a myriad of functional properties including superconductivity, magnetism, Mott transitions, multiferroicity and emergent behaviour at picoscale-designed interfaces. Current opportunities and challenges are also addressed, including possible new discoveries of non-equilibrium phenomena and optical control of correlated quantum phases of transition metal oxides.