The idea of using individual molecules as active electronic components provided the impetus to develop a variety of experimental platforms to probe their electronic transport properties. Among these, single-molecule junctions in a metal-molecule-metal motif have contributed significantly to our fundamental understanding of the principles required to realize molecular-scale electronic components from resistive wires to reversible switches. The success of these techniques and the growing interest of other disciplines in single-molecule-level characterization are prompting new approaches to investigate metal-molecule-metal junctions with multiple probes. Going beyond electronic transport characterization, these new studies are highlighting both the fundamental and applied aspects of mechanical, optical and thermoelectric properties at the atomic and molecular scales. Furthermore, experimental demonstrations of quantum interference and manipulation of electronic and nuclear spins in single-molecule circuits are heralding new device concepts with no classical analogues. In this Review, we present the emerging methods being used to interrogate multiple properties in single molecule-based devices, detail how these measurements have advanced our understanding of the structure-function relationships in molecular junctions, and discuss the potential for future research and applications.