I will review the recent theoretical progress on novel types of anyons that go beyond the Majorana fermion paradigm. These arise as zero modes localized at defects in fractional quantum Hall states. These zero modes are characterized by a topological ground state degeneracy, and manipulating them can realize new types of non-abelian statistics, generalizing the well-known braiding rules of Majorana zero modes. I will discuss various realizations of such exotic zero modes, and some of their signatures.