Empirically, Type Ia supernovae are the most useful, precise, and mature tools for determining astronomical distances. Acting as calibrated candles they revealed the presence of dark energy and are being used to measure its properties. However, the nature of the SN Ia explosion, and the progenitors involved, have remained elusive, even after seven decades of research. But now new large surveys are bringing about a paradigm shift --- we can finally compare samples of hundreds of supernovae to isolate critical variables. As a result of this, and advances in modeling, breakthroughs in understanding all aspects of SNe Ia are finally starting to happen.

Invited review for Nature Communications. Final published version. Shortened, updated