Many early-forming asteroids differentiated, as a result of incorporating the heat-generating isotope 26Al, and experienced various kinds of volcanic activity. The Dawn spacecraft's investigation of the best-preserved of these asteroids, 4 Vesta, warrants a reappraisal of the factors controlling asteroid volcanism. We conclude that silicate melts were removed efficiently from the mantles of all asteroids by complex networks of small and large veins and dikes. This implies that only a few percent of the interior consisted of melt at any one time. Thus although large amounts of mantle melting may ultimately have occurred, “magma oceans”, in the sense of mantles containing many tens of percent of melt, can not have formed. The total rate of silicate melt production in an asteroid of a given size can be predicted as a function of time after formation. If magma were erupted directly to the surface it must have done so through a small number of major dikes, brittle fractures that penetrated the outer thermal boundary crustal layer ∼10 km deep within which heat was conducted to the surface fast enough that temperatures stayed below the silicate solidus. By modeling the link between magma flow rate and the stresses needed to keep fractures open and allow magma to rise through them without excessive cooling, we show that continuous eruptions direct from mantle to surface were impossible on asteroids with radii less than ∼190–250 km. Instead, magma must have accumulated, in sills at the base of the thermal boundary layer or in magma reservoirs in its lower part. Magma could then erupt intermittently to the surface from these steadily replenished reservoirs. The eruption rates from the reservoirs are not linked directly to the melt production rate in the mantle and could be very large, hundreds to thousands of m3 s−1, comparable to rates in historic basaltic eruptions on Earth. Many asteroid magmas are expected to have contained at least a few hundred ppm of volatiles. On asteroids with radii less than ∼100 km, the gases and small (sub-mm) pyroclastic melt droplets ejected in explosive eruptions as volatiles expanded into the surrounding vacuum will have had velocities exceeding escape speed. Only pyroclasts of at least cm size will have had small enough speeds to be retained on the surface. Asteroids significantly larger than ∼100 km in radius will have retained all pyroclasts, and most clasts will have reached the surface after passing through optically dense fire fountains. These clasts suffered negligible cooling and coalesced into lava ponds feeding lava flows. Only if eruption rates were low and volatile contents high will enough clasts have suffered sufficient cooling that spatter or cinder deposits formed. Thicknesses of lava flows are controlled by the acceleration due to gravity, surface slope, and the effective yield strength that lava develops due to cooling. Low gravity on asteroids caused flows to be thick and, coupled with high eruption rates, induced initially turbulent flow. Cooling caused a change to laminar flow and eventually brought flows to a halt, but comparison of expected cooling rates and flow thicknesses suggests that many flows attained lengths of tens of km and stopped as a result of cessation of magma supply from the reservoir rather than cooling. If more than ∼30% melting of the mantle of an asteroid occurred and the resulting erupted volcanic products were retained on the surface, as is expected for asteroids with radii >∼100 km, the volcanic deposits will have buried the original chondritic surface layers of the asteroid to such great depths that they were melted, or at least heavily thermally metamorphosed, leaving no meteoritical evidence of their existence today. Tidal stresses caused by close encounters between asteroids and proto-planets may have briefly and temporarily increased melting and melt migration speeds in asteroid interiors but will not greatly have changed volcanic histories unless gross structural disruption took place.