Substructural logics are logics with restricted use of structural rules like weakening, contraction and exchange. There are several motivations for investigating substructural logics from the study of algebraic structures like residuated (semi)lattices to the study of type systems which allow for greater control over the number of times and the order in which variables are used.

Enriched with fixed point operators, these logics are highly expressive. In this talk, I will give a brief overview of substructural logics with fixed points and concentrate specifically on linear logic with fixed points discussing various proof systems, their expressivity, and semantics.