Braided subfactors of von Neumann algebras provide a framework for studying
two dimensional conformal field theories and their modular invariants. We
review this in the context of SU(3) conformal field theories through
corresponding SU(3) braided subfactors and various subfactor invariants
including spectral measures for the nimrep graphs, A_2-planar algebras and
almost Calabi-Yau algebras.Comment: 45 pages, 25 figures. v3: minor correction to Figure 14; v2: figures
of 0-1 parts of graphs included, some minor correction
