KLU is a set of routines from SuiteSparse for solving sparse linear systems. Eigen already supports the UMFPack routines from SuiteSparse, and it seems natural to support KLU as well. The KLU library is designed for circuit simulation or other extremely sparse systems. Additionally, a non-technical advantage it provides over UMFPack is that it is licensed under LGPL, rather than UMFPack's GPL.
As far as implementation goes, I based everything on the existing UMFPack work, which made things fairly straightforward.
There are still missing features in the implementation, namely the calculation of the determinant and the extraction methods.