  In two-dimensional conformal field theory (CFT) the building blocks are given
by chiral CFTs, i.e.~CFTs on the unit circle (compactified light-ray). They are
generated by quantum fields depending on one light-ray coordinate only. There
are two mathematical formulations of chiral CFT, the one based on vertex
operator algebras (VOAs) and the one based on conformal nets. We describe some
recent results which, for first time, gives a general construction of conformal
nets from (unitary) VOAs.
