Future sea level rise associated to global warming is one of the greatest societal and environmental challenges of tomorrow. A large part of the contribution comes from glaciers and ice sheets discharging ice and meltwater into the ocean and the recent worldwide increase is worrying. Future predictions of sea level rise try to encompass the complex processes of ice dynamics through glacier modelling but there are still large uncertainties due to the lack of observations or too coarse parameterisation, particularly for processes occurring at the glacier interfaces with the bed (sliding) and with the ocean (calving). This thesis focuses on modelling these processes from two marine-terminating glaciers in Svalbard, Kronebreen and Tunabreen. By inverting three years of high temporal resolution time-series of surface velocities on Kronebreen, basal properties are retrieved with the ice flow model Elmer/Ice in Paper I. Results suggest that surface melt during the summer greatly influences the dynamics of the following season and that sliding laws for such glaciers should be adapted to local and global processes changing in space and time. The subglacial drainage system, fed by the surface melt, is modelled in Paper II during two melting seasons. Results show different configurations of efficient and inefficient drainage systems between years and the importance of using a sliding law dependent on spatio-temporal changes in effective pressure. The interaction with the ocean is incorporated in Paper III by combining a series of models, including an ice flow model, a plume model and a particle model for discrete calving and compares the output with observations. Results show the importance of glacier geometry, sliding and undercutting on calving rate and location. However, more observations and analytic methods are needed. Time-lapse imagery placed in front of Tunabreen have been deployed and a method of automatic detection for iceberg calving is presented in Paper IV. Results show the influence of the rising plume in calving and the front destabilisation of the local neighbourhood.