Plasmonic metasurfaces based on ensembles of distributed metallic nanostructures can absorb, scatter, and in other ways shape light at the nanoscale. Forming hybrid plasmonic metasurfaces by combination with other materials opens up for new research directions and novel applications. This perspective highlights some of the recent advancements in this vibrant research field. Particular emphasis is put on hybrid plasmonic metasurfaces comprising organic materials and on concepts related to switchable surfaces, light-to-heat conversion, and hybridized light-matter states based on strong coupling.