We give an overview about local conformal nets on the circle as considered by Kawahigashi, Longo, Müger, Rehren et al. The motivation to study these objects arises not only from mathematical physics, but also from subfactor theory and recently also from topological field theories. Conformal nets carry a very rich structure. For example, their representation category is a braided tensor category, which turns out to be a modular tensor category in interesting examples. Recent developments in TQFTs by Hopkins and Lurie connect a coordinate free variant of conformal nets developed by Bartels, Henriques and Douglas to local TQFTs.