Floer theoretic invariants with support

I will give a survey talk on Floer theoretic invariants with support, highlighting recent developments. I will go over the case where the ambient symplectic manifold is equipped with a complete finite type Liouville structure and the support can be any closed (possibly compact) subset that is conical at infinity. This will include both open and closed string theory. Special attention will be given to the operadic structures. Then I will explain how to extend these constructions to closed symplectic manifolds and compact supports. I will end with a discussion of locality and descent. This includes joint work with many people.