The work in this thesis concentrates on Katla volcano in southern Iceland. This is one of Europe’s most active volcanoes and its history tells us that it poses many threats to society, both locally (Iceland) and on a broader scale (Europe). Its geological setting is complex, where the effects of a melting anomaly in the mantle and a changing rift geometry, perturb the classical setting of volcanism in a rifting setting. The work has focused on two aspects. The first is the varying distribution of physical properties in the subsurface around the volcano. The second is the distribution of microearthquakes around the volcano. The physical properties that we study are the speeds of seismic waves that reflect variations of temperature, composition and fracturing of the rocks. These can, therefore, help us learn about long-term processes in the volcano. The seismicity gives shorter-term information about deformation associated with current processes. I have applied two tomographic techniques to study Katla’s subsurface to a depth of 5-10 km, namely local-earthquake and ambient-noise tomography. The former makes use of the timing of waves generated by local earthquakes to constrain the earthquakes’ locations and the distribution of wave speed. Here I have concentrated on compressional waves or P waves with a typical frequency content around 10 Hz. With the latter, surface waves are extracted from microseismic noise that is generated far away at sea and their timing is measured to constrain their wave-speed distribution, which then is used to map shear-wave velocity variations. This is done at a typical frequency of 0.3 Hz. I find that the volcano contains rocks of higher velocity than its surroundings, that Katla’s caldera is underlain by low velocities at shallow depth that may be explained by hot or partially molten rocks and that beneath the caldera lies a volume of particularly high velocities that may constitute differentiated cumulates. But, I also find that it is not simple to compare results from such different wave types and discuss a number of complications in that regard. In addition to the well-known microearthquake distribution in the caldera region of Katla and to its west, we have discovered two additional areas of microearthquake activity on the volcano’s flanks, south and east of the caldera. These point to current activity and are, therefore, of interest from a hazard point of view. However, it is difficult to pinpoint their underlying process. Speculation about possible interpretation leads me to hydrothermal processes or small pockets of melt ascending due to their buoyancy or locally enhancing fluid pressure, thereby lowering the effective stress.