  A combination of analytic and numerical methods has yielded a clear
understanding of the approach to the singularity in spatially inhomogeneous
cosmologies. Strong support is found for the longstanding claim by Belinskii,
Khalatnikov, and Lifshitz that the collapse is dominated by local Kasner or
Mixmaster behavior. The Method of Consistent Potentials is used to establish
the consistency of asymptotic velocity term dominance (AVTD) (local Kasner
behavior) in that no terms in Einstein's equations will grow exponentially when
the VTD solution, obtained by neglecting all terms containing spatial
derivatives, is substituted into the full equations. When the VTD solution is
inconsistent, the exponential terms act dynamically as potentials either to
drive the system into a consistent AVTD regime or to maintain an oscillatory
approach to the singularity.
