Whether or not we know just how they work, type Ia Supernovae (SNe Ia) are held to be great standard candles for building our cosmic distance ladder. In so many cases where we can check their distance by other, more fundamental means there seems to be a very nice trend we can use.
The theory behind these guys is described by the Chandrasekhar limit, that is, the maximum density at which you can compact an object before the gravity overwhelms internal support forces. For white dwarfs (the dead cores of many stars not massive enough to have gone supernova as they died), they all have a similar radius so usually we just talk about the mass limit as being 1.4 times the mass of the Sun. Any more massive and it would have gone supernova in the first place (a Type II Supernova). If a white dwarf is just under that limit and a companion star dumps enough on it to go over the limit, then a SNe Ia happens.
This is a good fit to all the data, but most importantly because SNe Ia don't have much, if any, hydrogen in their spectra which means that they can't be main sequence stars that still have their envelope of hydrogen.
But as to every story, there's some exceptions.
Back in 2003 a supernova with the exciting name of SNLS-03D3bb occurred that was more than twice as bright as SNe Ia's should be. It wasn't reported until 2006 and that same year, another group (Howell et al.) inferred a mass of the pre-explosion core to be 2.1 times the mass of the Sun!
Ok. Whatever. We'll tweak the model. Maybe these guys were just spinning faster than normal SNe Ia's which would give them some extra support before the collapse thanks to centrifugal forces. Maybe mass just got dumped on extra fast, as in two white dwarfs colliding. Maybe differential rotation was more important than expected and really does need to be included in the basic model. Maybe the metallicity is somehow really important. Perhaps the orbital period of the white dwarf and the donor star plays an important role. Who knows?
So group decided to try to put some constraints on the problem by adding some of these things to the models and trying it out a bunch of different ways.
While they haven't completely solved the problem, the did learn four things:
1) If the white dwarf starts off at around ~one solar mass (like most probably are) the resultant supernovae are very uniform, right at the 1.4 limit.
2) If the white dwarf is close to 1.2 solar masses to start, the final mass before going supernova can creep up to nearly 1.8 solar masses. Getting there but not good enough.
3) To be consistently above the 1.6 solar masses, the donor star must be 2.2 - 3.3 solar masses and in a very short orbit of 0.5 - 4 days. Smaller and shorter if the donor is metal poor.
4) Metallicity is important. Metal poor stars are less likely to make these super-Chandrasekhar supernovae. This one's perhaps the most imminently important one because this means that we're less likely to be having these oddballs contaminating our data at high redshifts (ie, really far away) which is where they're the most useful (remember, we have other ways to check distances nearby).
So the problem's not solved, but such is the nature of science.
Chen, W., & Li, X. (2009). ON THE PROGENITORS OF SUPER-CHANDRASEKHAR MASS TYPE Ia SUPERNOVAE The Astrophysical Journal, 702 (1), 686-691 DOI: 10.1088/0004-637X/702/1/686