Field observations and geophysical data indicate that many igneous bodies grow by amalgamation of successive magma pulses that commonly take the shape of horizontal sheets (sills). Emplacement styles and emplacement rates of magma bodies have fundamental implications on magma differentiation, country rock metamorphism and assimilation, and for the formation of large magma chambers in the upper crust. When a magma body begins to grow by slow accretion of sills, each successive intrusion solidifies before the injection of the next one. When the system is thermally mature, sill temperatures equilibrate above the solidus, melts accumulate and older sills can re-melt. The time needed for each magma injection to cool down and equilibrate with its surrounding is short relatively to the total emplacement time of the body. The transition from a mafic crystal-poor magma to a partially molten rock that retains a highly differentiated melt is fast, whereas the resulting evolved residual melt can reside in the crust for protracted periods. As long as temperatures in the system are relatively low, highly differentiated melts are generated, which may explain the bi-modal character and the absence of intermediate compositions in some magmatic provinces. The level of emplacement of successive magma pulses controls the shape of the thermal anomaly associated with the magma body growth. Metamorphism, partial melting and assimilation of the country rock are favoured if successive magma sheets are emplaced at or close to the country rock–magma body boundary. If the magma emplacement rate is low, the size of the thermal aureole is controlled by the size of one pulse and not by the size of the entire igneous body. Understanding emplacement of magma bodies is fundamental for our understanding of the plutonism– volcanism relationship. Magma emplacement rates of several centimetres per year are needed for a magma body to evolve into a large magma chamber able to feed large silicic explosive eruptions. The time-averaged emplacement rates of plutons are lower than this critical emplacement rate. Eruptions of 100s to 1000s cubic kilometres of silicic products show that such high volumes of magmas can accumulate in the upper crust. This suggests that the emplacement of magma bodies is a multi-timescale process with the development of large magma chambers corresponding to the highest magma fluxes. Because they control magmatic processes and the impact of magma intrusion on the country rock, future studies should focus on magma emplacement rates and on magma emplacement geometries. These studies should integrate field observation on plutons and geophysical data on active magmatic systems, coupled with laboratory experiments and numerical simulations.