The strong enhancement and localization of electromagnetic field in plasmonic systems have found applications in many areas, which include sensing and biosensing. In this paper, an overview will be provided of the use of plasmonic phenomena in sensors and biosensors with emphasis on two main topics. The first is related to possible ways to enhance the performance of sensors and biosensors based on surface plasmon resonance (SPR), where examples are given of functionalized magnetic nanoparticles, magnetoplasmonic effects and use of metamaterials for SPR sensing. The other topic is focused on surface-enhanced Raman scattering (SERS) for sensing, for which uniform, flexible, and reproducible SERS substrates have been produced. With such recent developments, there is the prospect of improving sensitivity and lowering the limit of detection in order to overcome the limitations inherent in ultrasensitive detection of chemical and biological analytes, especially at single molecule levels.