For 40 years, the case for the existence of carbonate magmas rested on field observations of carbonatite intrusions, in which the lack of thermal effects raised an apparent conflict with the high melting temperatures of pure carbonates. Since 1960, the position has changed, with the growth of experimental studies and increasing observations of effusive carbonate rocks. A nephelinite/phonolite volcano in Tanzania is currently erupting Na-Ca-K carbonate magma (around 600°C). This is unlike all other intrusive and effusive carbonatites (350 examples worldwide) which are dominantly composed of Ca, Mg, Fe carbonates, and have negligible alkali contents. Although a number of effusive calcio–carbonatites are considered to be degraded alkali carbonatites, there are several examples (including one magnesio-carbonatite) which are close to their erupted composition, and substantiate the existence of high T carbonate magmas lacking essential alkalis at the time of eruption. In these associations silicate magmas are absent (or minor), and in most the effusive carbonatites have been erupted directly from the mantle (with entrained peridotite debris and minerals). They provide a link with the ultramafic association (peridotite and pyroxenite), seen in some carbonatite intrusions, with the commonly associated ultramafic lamprophyres (which may also carry mantle xenoliths), and with carbonate-rich kimberlites. Many carbonatite intrusions also have little or no associated silicate magmas, putting in question a popular view that carbonatites normally form only minor parts of alkaline igneous complexes of nephelinite/phonolite type. The corollary, that the carbonatites are normally differentiates is even less sound, because in alkaline complexes the carbonatite is always last in the eruption sequence. Here the carbonatite may represent the final residua expelled from the source region. Most large carbonatite intrusions seem to have been emplaced at lower T than effusives, probably as a near-solidus mush, with the interstitial fluid metasomatizing the country rocks. A wider perspective of carbonate magma genesis is called for, to encompass various kinds of differentiation from alkaline silicate magmas, and primary carbonate magmas from various depths in the mantle (with or without silicate melts). The strongly bimodal composition distribution of calcic and dolomitic carbonatites is a further factor awaiting explanation. Half of the known carbonatites are in Africa, and their timing and distribution indicate that the activity is a response to lateral forces acting across the plate. Carbonate magmatism is waiting to be unleashed. This activity demands attention because it is now clear that carbonate magmatism is a crucial surface expression of deep mantle processes.