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The flame born in the deep interior of a white dwarf that becomes a Type Iasupernova is subject to several instabilities. We briefly review theseinstabilities and the corresponding flame acceleration. We discuss theconditions necessary for each of the currently proposed explosion mechanismsand the attendant uncertainties. A grid of critical masses for detonation inthe range $10^7$ - $2 \times 10^9$ g cm$^{-3}$ is calculated and itssensitivity to composition explored. Prompt detonations are physicallyimprobable and appear unlikely on observational grounds. Simple deflagrationsrequire some means of boosting the flame speed beyond what currently exists inthe literature. ``Active turbulent combustion'' and multi-point ignition arepresented as two plausible ways of doing this. A deflagration that moves at the``Sharp-Wheeler'' speed, $0.1 g_{\rm eff} t$, is calculated in one dimensionand shows that a healthy explosion is possible in a simple deflagration if thefront moves with the speed of the fastest floating bubbles. The relevance ofthe transition to the ``distributed burning regime'' is discussed for delayeddetonations. No model emerges without difficulties, but detonation in thedistributed regime is plausible, will produce intermediate mass elements, andwarrants further study.Comment: 28 pages, 4 figures included, uses aaspp4.sty. Submitted to Ap

The Thermonuclear Explosion of Chandrasekhar Mass White Dwarfs