In 1993, Schellekens obtained a partial classification of holomorphic vertex operator algebras of central charge 24 by determining possible Lie algebra structures for the weight one subspaces. There are 71 cases in his list. In addition, it seems that the Lie algebra structure of the weight one subspace determines the holomorphic vertex operator algebra structure uniquely. This would be an analogue of the uniqueness of the Niemeier lattices: a positive-definite even unimodular lattice of rank 24 is uniquely determined by the root system consisting of norm 2 vectors.
In this talk, I explain recent progress based on joint works with C.H. Lam, and discuss remaining problems.