Magmatic processes have played, and still play, a key role in the evolution of Earth. Their surface manifestations via explosive eruptions that propel gases and ashes high into the atmosphere, or high-temperature geothermal fields that fuel power plants, continuously remind us that our planet is still active, striving daily to dissipate its internal energy via upward transport of hot material. Despite decades of intensive research, the largely hidden nature of source processes driving magmas has hampered our quantitative understanding of this phenomenon. Answering fundamental questions such as the lifetime of a magmatic system, the occurrence and style of the next eruptive episode of volcanoes still requires a wealth of assumptions or simplifications that almost always limit current model predictions to qualitative assessments at best.