  The fractional quantum Hall (FQH) effect gives rise to abundant topological
phases, presenting an ultimate platform for studying the transport of edge
states. Generic FQH edge contains multiple edge modes, commonly including the
counter-propagating ones. A question of the influence of Anderson localization
on transport through such edges arises. Recent experimental advances in
engineering novel devices with interfaces of different FQH states enable
transport measurements of FQH edges and edge junctions also featuring
counter-propagating modes. These developments provide an additional strong
motivation for the theoretical study of the effects of localization on generic
edge states. We develop a general framework for analyzing transport in various
regimes that also naturally includes localization. Using a reduced field theory
of the edge after localization, we derive a general formula for the
conductance. We apply this framework to analyze various experimentally relevant
geometries of FQH edges and edge junctions.
