This includes notably the invention and study of homotopy-coherent structures such as A-infinity operads, A-infinity algebras and L-infinity-algebras and their application to BV theory, string field theory (longer list of links should eventually go here).
The above survey lists key concepts and collects references to further literature.
Essentially using variants of the Dold-Kan correspondence one may regard many of these differential graded algebra structures as higher categorical structures. For instance the pretriangulated dg-categories formed by homotopy coherent structures are presentations for stable (infinity,1)-categories.
In this sense “cohomological physics” is understood as part of n-categorical physics.