Several progenitor scenarios have been suggested for Type Ia supernovae. Here we discuss the consequences for the explosion mechanism and for observables of some of them, which are explored by means of multi-dimensional hydrodynamic and radiation transfer simulations. While the observables predicted from delayed detonations of Chandrasekhar-mass white dwarfs agree reasonably well with the data, the corresponding progenitor systems may be too rare to account for the observed rate of Type Ia supernovae. Several alternatives are investigated of which violent mergers of two white dwarfs and, perhaps, double detonations of sub-Chandrasekhar mass white dwarfs hold promise for reproducing the observables of normal Type Ia supernovae.