Exceptional points (EPs), representing non-Hermitian singularities where eigenvalues and eigenvectors coalesce, have emerged as an intriguing concept in modern physics. Their unique topological and asymmetric responses have enabled new pathways for controlling wave propagation, sensing, and signal processing. Among the diverse platforms, plasmonic systems have proven especially attractive, as their inherent loss, strong dispersion, and tunable resonances and coupling can be utilized to tailor EPs at the subwavelength scale. In this review, we provide a comprehensive overview of recent advances at the intersection of EP physics and plasmonics. We first introduce the mathematical and physical foundations of EPs in non-Hermitian systems. We then discuss key experimental and theoretical developments in plasmonic EPs, including polarization manipulation, asymmetric wavefront control, mode conversion, and enhanced sensitivity. Particular attention is given to strategies that exploit symmetry breaking, loss engineering, and geometric phases to realize novel and robust EP-driven functionalities. Finally, we discuss emerging trends, such as the use of EP pairs for full vectorial control and the integration of non-Hermitian plasmonic structures with tunable, active, and even nonreciprocal thermal emission. By reframing loss as a design resource and leveraging the Riemann-surface geometry of non-Hermitian spectra, plasmonic EPs offer a new route to compact, robust, and programmable nanophotonic devices.