Despite their relevance across a broad range of astrophysical research topics, Type Ia supernova explosions are still poorly understood and answers to the questions of when, why and how these events are triggered remain unclear. In this respect, polarisation offers a unique opportunity to discriminate between the variety of possible scenarios. The observational evidence that Type Ia supernovae are associated with rather low polarisation signals (smaller than a few per cent) places strong constraints for models and calls for modest asphericities in the progenitor system and/or explosion mechanism.The goal of this thesis is to assess the validity of contemporary Type Ia supernova explosion models by testing whether their predicted polarisation signatures can account for the small signals usually observed. To this end, we have implemented and tested an innovative Monte Carlo scheme in the radiative transfer code artis. Compared to previous Monte Carlo approaches, this technique produces synthetic observables (light curves, flux and polarisation spectra) with a substantial reduction in the Monte Carlo noise and therefore in the required computing time. This improvement is particularly crucial for our study as we aim to extract very weak polarisation signals, comparable to those detected in Type Ia supernovae. We have also demonstrated the applicability of this method to other classes of supernovae via a preliminary study of the first spectropolarimetry observations of superluminous supernovae.Using this scheme, we have calculated synthetic spectropolarimetry for three multi-dimensional explosion models recently proposed as promising candidates to explain Type Ia supernovae. Our findings highlight the power of spectropolarimetry in testing and discriminating between different scenarios. While all the three models predict light curves and flux spectra that are similar to each others and reproduce those observed in Type Ia supernovae comparably well, polarisation does provide a clear distinction. In particular, we find that one model is too strongly asymmetric and produces polarisation levels that are too high and clearly inconsistent with those detected for the bulk of Type Ia supernovae. Polarisation signals - and their time evolution - extracted for the remaining two models are instead in good agreement with the currently available spectropolarimetry data. Providing a powerful way to connect hydrodynamic explosion models to observed data, the study presented in this thesis is an important step towards a better understanding of Type Ia supernovae from a synthesis of theory and observations.