Localized Surface plasmon resonance (LSPR) sensors based on metal nanoparticles, a mode of signal transduction, and biological LSPR sensors, concerned with label-free detection, are studied. To find the functional form of the LSPR peak wavelength's dependence on the dielectric function of the medium, the analytical, frequency-dependent form from the Drude model of the electronic structure of metals is used. LSPR directly detects the target's refractive index and so it is a label-free sensor, in which the measured signal is due only to the presence of the target molecule. LSPR sensing is used to probe biomolecular interactions including nucleic acid hybridization and protein-carbohydrate, cytochrome-inhibitor, aptamer, protein, and toxinreceptor interactions. A scheme for LSPR-based gas sensing is developed by Karakouz et al., in which evaporated gold island films are coated with the polymers polystyrene sulfonic acid (PSS) and polystyrene (PS).