<p>Magmatic systems are composed of many nonlinearly interacting components that operate across various scales; thus, these systems can be modelled as complex systems. In this Perspective, we examine efforts to recognize and model complexity in magmatic systems and suggest the direction for building a global integrated model to investigate volcanic and igneous processes. Magmatic systems are complex, as they operate on time and spatial scales ranging from seconds to millions of years and micrometres to kilometres, respectively, organized as networks of interacting components. These networks drain magmas and volatiles from deep sources towards plutons, dykes, sills, and volcanoes. Statistical analyses suggest power-law relationships in magmatic and volcanic processes, from the geometrical feature of melt extraction network at the source, to magma mingling, to the distribution of eruption intensity. These findings serve as evidence for self-organized criticality, suggesting that magmatic systems respond to small disturbances in unpredictable ways. The behaviours of complex systems emerge from the connections between the&#xa0;parts of the system and cannot be predicted by separate investigation of the&#xa0;individual parts. Therefore, Earth science should follow the example of fields such as climate sciences and take advantage of tools developed in complex system science to build an integrated model to test the validity of conceptual models and advance understanding of magmatic systems.</p>