Biosensing requires fast, selective, and highly sensitive real-time detection of biomolecules using efficient simple-to-use techniques. Due to a unique capability to focus light at nanoscale, plasmonic nanostructures provide an excellent platform for label-free detection of molecular adsorption by sensing tiny changes in the local refractive index or by enhancing the light-induced processes in adjacent biomolecules. This review discusses the opportunities provided by surface plasmon resonance in probing the chirality of biomolecules as well as their conformations and orientations. Various types of chiral plasmonic nanostructures and the most recent developments in the field of chiral plasmonics related to biosensing are considered.