Localized surface plasmon resonance (LSPR) is a nanoscale phenomenon associated with noble metal nanostructures that has long been studied and has gained considerable interest in recent years. These resonances produce sharp spectral absorption and scattering peaks, along with strong electromagnetic near-field enhancements. Over the past decade, advancements in the fabrication of noble metal nanostructures have propelled significant developments in various scientific and technological aspects of LSPR. One notable application is the detection of molecular interactions near the nanoparticle surface, observable through shifts in the LSPR spectral peak. This document provides an overview of this sensing strategy. Given the broad and expanding scope of this topic, it is impossible to cover every aspect comprehensively in this review. However, we aim to outline major research efforts within the field and review a diverse array of relevant literature. We will provide a detailed summary of the physical principles underlying LSPR sensing and address some existing inconsistencies in the nomenclature used. Our discussion will primarily focus on LSPR sensors that employ metal nanoparticles, rather than on those utilizing extended, fabricated structures. We will concentrate on sensors where LSPR acts as the primary mode of signal transduction, excluding hybrid strategies like those combining LSPR with fluorescence. Additionally, our examination of biological LSPR sensors will largely pertain to label-free detection methods, rather than those that use metal nanoparticles as labels or as means to enhance the efficacy of a label. In the subsequent section of this review, we delve into the analytical theory underpinning LSPR, exploring its physical origins and its dependency on the material properties of noble metals and the surrounding refractive index. We will discuss the behavior of both spherical and spheroidal particles and elaborate on how the LSPR response varies with particle aspect ratio. Further, we detail the fundamentals of nanoparticle-based LSPR sensing. This includes an exploration of single-particle and ensemble measurements and a comparative analysis of scattering, absorption, and extinction phenomena. The discussion will extend to how these principles are applied in practical sensing scenarios, highlighting the key experimental approaches and measurement techniques.