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Large gas bubbles can reach the surface of pools of mud and lava where they burst, often through the formation and expansion of circular holes. Bursting bubbles release volatiles and generate spatter, and hence play a key role in volcanic degassing and volcanic edifice construction. Here, we study the ascent and rupture of bubbles using a combination of field observations at Pâclele Mici (Romania), laboratory experiments with mud from the Imperial Valley (California, USA), numerical simulations and theoretical models. Numerical simulations predict that bubbles ascend through the mud as elliptical caps that develop a dimple at the apex as they impinge on the free surface. We documented the rupture of bubbles in nature and under laboratory conditions using high-speed video. The bursting of mud bubbles starts with the nucleation of multiple holes, which form at a near-constant rate and in quick succession. The quasi-circular holes rapidly grow and coalesce, and the sheet evolves towards a filamentous structure that finally falls back into the mud pool, sometimes breaking up into droplets. The rate of expansion of holes in the sheet can be explained by a generalization of the Taylor-Culick theory, which is shown to hold independent of the fluid rheology.