Despite the importance of Type Ia supernovae (SNe Ia) for modern astrophysics, their detailed mechanism is still not fully understood. In this contribution, we present recent findings from numerical explosion models in the context of the observed diversity of SNe Ia and we discuss how these models can help to shed light on the explosion mechanism and the progenitor stars of SNe Ia. In addition, we introduce the Heidelberg Supernova Model Archive (HESMA), a new online data base where we provide integrated isotopic abundances and radially averaged ejecta profiles and synthetic observables for a wide range of state-of-the-art explosion models.
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