  We discuss what has been achieved in the past twenty years on the
construction and study of a braided finite tensor category structure on a
suitable module category for a suitable vertex operator algebra. We identify
the main difficult parts in the construction, discuss the methods developed to
overcome these difficulties and present some further problems that still need
to be solved. We also choose to discuss three among the numerous applications
of the construction.

Quantum Algebra;High Energy Physics - Theory;Category Theory