Over the last few decades, significant advances in using geophysical techniques to image the structure of magma plumbing systems have enabled the identification of zones of melt accumulation, crystal mush development, and magma migration. Combining advanced geophysical observations with petrological and geochemical data has arguably revolutionised our understanding of, and afforded exciting new insights into, the development of entire magma plumbing systems. However, divisions between the scales and physical settings over which these geophysical, petrological, and geochemical methods are applied still remain. To characterise some of these differences and promote the benefits of further integration between these methodologies, we provide a review of geophysical techniques and discuss how they can be utilised to provide a structural context for and place physical limits on the chemical evolution of magma plumbing systems. For example, we examine how Interferometric Synthetic Aperture Radar (InSAR), coupled with Global Positioning System (GPS) and Global Navigation Satellite System (GNSS) data, and seismicity may be used to track magma migration in near real-time. We also discuss how seismic imaging, gravimetry and electromagnetic data can identify contemporary melt zones, magma reservoirs and/or crystal mushes. These techniques complement seismic reflection data and rock magnetic analyses that delimit the structure and emplacement of ancient magma plumbing systems. For each of these techniques, with the addition of full-waveform inversion (FWI), the use of Unmanned Aerial Vehicles (UAVs) and the integration of geophysics with numerical modelling, we discuss potential future directions. We show that approaching problems concerning magma plumbing systems from an integrated petrological, geochemical, and geophysical perspective will undoubtedly yield important scientific advances, providing exciting future opportunities for the volcanological community.