Recent developments have greatly improved the sensitivity of optical sensors based on metal nanoparticle arrays and single nanoparticles. We introduce the localized surface plasmon resonance (LSPR) sensor and describe how its exquisite sensitivity to size, shape and environment can be harnessed to detect molecular binding events and changes in molecular conformation. We then describe recent progress in three areas representing the most significant challenges: pushing sensitivity towards the single-molecule detection limit, combining LSPR with complementary molecular identification techniques such as surface-enhanced Raman spectroscopy, and practical development of sensors and instrumentation for routine use and high-throughput detection. This review highlights several exceptionally promising research directions and discusses how diverse applications of plasmonic nanoparticles can be integrated in the near future.