Forecasting eruptions is a fundamental goal of volcanology. However,difficulties in identifying eruptive precursors, fragmented approachesand lack of resources make eruption forecasting difficult to achieve.In this Review, we explore the first-order scientific approaches thatare essential to progress towards forecasting the time and location ofmagmatic eruptions. Forecasting in time uses different monitoringtechniques, depending on the conduit-opening mode. Ascendingmagma can create a new conduit (closed-conduit eruptions), usea previously open conduit (open-conduit eruptions) or flow below asolidified magma plug (semi-open-conduit eruptions). Closed-conduiteruptions provide stronger monitoring signals often detected monthsin advance, but they commonly occur at volcanoes with poorlyknown pre-eruptive behaviour. Open-conduit eruptions, associatedwith low-viscosity magmas, provide more subtle signals oftendetected only minutes in advance, although their higher eruptionfrequency promotes more testable approaches. Semi-open-conduiteruptions show intermediate behaviours, potentially displaying clearpre-eruptive signals days in advance and often recurring repeatedly.However, any given volcano can experience multiple conduit-openingmodes, sometimes simultaneously, requiring combinations offorecasting approaches. Forecasting the location of vent openingrelies on determining the stresses controlling magma propagation,deformation and seismic monitoring. The use of physics-based modelsto assimilate monitoring data and observations will substantiallyimprove forecasting, but requires a deeper understanding ofpre-eruptive processes and more extensive monitoring data.