at my school what I've seen is that they mostly do physical chemistry of biopolymers: structure, dynamics, analytical techniques.
there's a lot of overlap with physical chemistry and materials science in things like biomaterials and polymer dynamics. they also use a lot of the same analytical techniques like nuclear magnetic resonance, atomic force microscopy and UV-vis spectroscopy. the main research is in single molecule reaction kinetics, properties and applications of biomaterials, use of biological polymers in (nonmedical related) nanotechnology, and design of biosensors.
there is also computational work about biopolymer folding and interaction with other biopolymers, as well as biopolymer interactions with inorganic surfaces.
other than that, there's some more unconventional research like biophotonics which i don't really understand the point of nor see any practical application to, but its there.