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Volcanoes and glaciers can both pose a significant threat to life and property. Volcanoes can erupt suddenly, without warning, causing injury, death and damage to property. Glaciers generally present a hazard over longer timescales, melting or sliding into the oceans and contributing to sea-level rise. The movement of melt at volcanoes, and ice at and near the Earth's poles, can be investigated using microseismicity, emitted when these fluids and bodies release kinetic energy as they move. I use this microseismicity to study: melt moving from the deep crust and feeding Bardarbunga volcano, Iceland, before and after an eruption; icequakes at the bed of glaciers and ice sheets to study and constrain the physics of glacial sliding; and surface icequakes caused by crevassing, to see whether or not the crevasses observed are induced by hydrofracture. I use a combination of seismic observations and simple physical models to investigate these fundamental geophysical processes. Understanding the magmatic plumbing of a volcano is important for attempting to improve eruption forecasting. I analyse microseismicity before and after the Bardarbunga volcanic eruption, the largest eruption in Iceland in 230 years, to study possible pathways of melt from the deep crust to the shallow melt storage region. The seismicity and earthquake source mechanisms suggest that melt travels along a pathway that is approximately vertical, and laterally offset from the main shallow melt storage region by 12 km. However, it is also likely that an aseismic melt feed exists directly under Bardarbunga that we do not observe. These observations imply that volcanoes can be fed from depth, with lateral offsets of 10s kms, and that it is not adequate to monitor such volcanoes using seismicity alone. One critical process for constraining sea-level rise projections is glacial sliding. I describe how to detect and locate icequakes that originate at the bed of glaciers, which can be used to study glacial sliding. I analyse icequake source mechanisms for several glacial settings, comprising a range of spatial scales, in an attempt to unify the theory of stick-slip icequake failure, what it can tell us about glacial slip, and how such icequakes can be used to provide the first remotely measured values of bed shear modulus. The method used to remotely measure bed shear modulus will help constrain ice dynamics models and inform future passive cryoseismology studies of the Earth's ice sheets. Another poorly understood process is surface crevassing. Again, I analyse the source mechanisms of surface crevassing icequakes and show that they are tensile cracks, opening in the shallow subsurface. I present a novel method of obtaining depth estimates for these crevasse icequakes. Deriving crevasse depth is important since crevasse depth is usually limited by the stress distribution within the ice column, unless they are filled with water that can allow deeper propagation via hydrofracture. This mechanism is a possible pathway of meltwater propagating from surface to bed, lubricating the bed and exacerbating the movement of ice into the ocean. The same mechanism is also important for understanding how ice shelves, such as the Larson B ice shelf, break up, releasing onshore ice to flow unperturbed into the ocean. Such observations of crevasse fracture are therefore of great relevance for understanding key instabilities that could contribute to future sea-level changes. My results help inform our understanding of the aforementioned processes, which are critical for forecasting volcanic eruptions better, and informing and constraining ice dynamics models used for sea-level rise projections.