Models for Type Ia supernovae and related astrophysical transients

We give an overview of recent efforts to model Type Ia supernovae and related astrophysical transients resulting from thermonuclear explosions in white dwarfs. In particular we point out the challenges resulting from the multi-physics multi-scale nature of the problem and discuss possible numerical approaches to meet them in hydrodynamical explosion simulations and radiative transfer modeling. We give examples of how these methods are applied to several explosion scenarios that have been proposed to explain distinct subsets or, in some cases, the majority of the observed events. In case we comment on some of the successes and shortcoming of these scenarios and highlight important outstanding issues.Comment: 20 pages, 2 figures, review published in Space Science Reviews as part of the topical collection on supernovae, replacement corrects typos in the conclusions sectio