Most exploding white dwarfs are normal type-Ia supernovae (SN Ia) that have proven so useful as standardizable candles to measure cosmic distances and discover the accelerating Universe. I will describe current cosmological applications of SN Ia and future prospects with upcoming flagship projects like LSST and WFIRST. The utility of SN Ia as distance indicators is limited by our lack of detailed physical understanding of these explosions. Observations have revealed that not all white dwarf supernovae are normal SN Ia. Unusual objects, including a class we call “type-Iax” supernovae, provide a window into the uncertain progenitors, binary companions, and explosion mechanisms of white dwarf supernovae, including the only example of a direct, pre-explosion observation of a progenitor system. Understanding these “peculiar cousins” to normal type-Ia supernovae may yield important clues to the nature of SN Ia and the variety of systems that result in white dwarf explosions.