Edges of gapped topological states may host gapless edge modes that cannot be realized as stand-alone systems. Examples include quantum Hall edge states, surface states of topological insulators and super-conductors, etc. In my talk I will examine situations in which these edge states form fractionalized phases of their own. Examples to be discussed include non-abelian defects in edges of abelian quantum Hall states, Haldane-type phases formed by these defects, and topologically ordered states on surfaces of weak topological insulators.