  Despite their prominent role in cosmography, little is yet known about the
nature of type-Ia supernovae (SNe Ia), from the identity of their progenitor
systems, through the evolution of those systems up to ignition and explosion,
and to the causes of the environmental dependences of their observed
properties. I briefly review some of those puzzles. I then focus on recent
progress in reconstructing the SN Ia delay time distribution (DTD) -- the SN
rate versus time that would follow a hypothetical brief burst of star
formation. A number of measurements of the DTD over the past two years, using
different methods and based on SNe Ia in different environments and redshift
ranges, are converging. At delays 1<t<10 Gyr, these measurements show a similar
1/t power-law shape, with similar normalizations. The DTD peaks at the shortest
delays probed, but there is still some uncertainty regarding its precise shape
in the range 0.1<t<1 Gyr. At face value, this result supports Ron Webbink's
(1984) idea of a double-degenerate progenitor origin for SNe Ia, but the
numbers currently predicted by binary population synthesis models must be
increased by factors of 3-10, at least. Single-degenerate progenitors may still
play a role in producing short-delay SNe Ia, or perhaps all SNe Ia, if there is
something important missing in the current modeling efforts.
