The original ‘proof’ fills 500 journal articles. An updated, self-contained proof is in the process of being written, and it is estimated that it will be 5000 pages long. As of 2008 six volumes had been published, out of an expected 11.
An original conceptual insight into the classification of finite groups from the point of algebraic geometry (involving embeddings into algebraic groups) has been recently achieved in an award-winning article
Michael J. Larsen, Richard Pink, Finite subgroups of algebraic groups, J. Amer. Math. Soc. 24 (2011), 1105-1158 doi