Plasmonic surface lattice resonances (SLRs) are mixed light-matter states emergent in a system of periodically arranged metallic nanoparticles (NPs) under the constraint that the array spacing is able to support a standing wave of optical-frequency light. The properties of SLRs derive from two separate physical effects; the electromagnetic (plasmonic) response of metal NPs and the electromagnetic states (photonic cavity modes) associated with the array of NPs. Metal NPs, especially free-electron metals such as silver, gold, aluminum, and alkali metals, support optical-frequency electron density oscillations known as localized surface plasmons (LSPs). The high density of conduction-band electrons in these metals gives rise to plasmon excitations that strongly couple to light even for particles that are several orders of magnitude smaller than the wavelength of the excitation source. In this sense, LSPs have the remarkable ability to squeeze far-field light into intensely localized electric near-fields that can enhance the intensity of light by factors of ∼103 or more. Moreover, as a result of advances in the synthesis and fabrication of NPs, the intrinsic dependence of LSPs on the NP geometry, composition, and size can readily be exploited to design NPs with a wide range of optical properties. One drawback in using LSPs to enhance optical, electronic, or chemical processes is the losses introduced into the system by dephasing and Ohmic damping-an effect that must either be tolerated or mitigated. Plasmonic SLRs enable the mitigation of loss effects through the coupling of LSPs to diffractive states that arise from arrays satisfying Bragg scattering conditions, also known as Rayleigh anomalies. Bragg modes are well-known for arrays of dielectric NPs, where they funnel and trap incoming light into the plane of the lattice, defining a photonic cavity. The low losses and narrow linewidths associated with dielectric NPs produce Bragg modes that oscillate for ∼103-104 cycles before decaying. These modes are of great interest to the metamaterials community but have relatively weak electric fields associated with dielectric NPs and therefore are not used for applications where local field enhancements are needed. Plasmonic lattices, i.e., photonic crystals composed of metallic NPs, combine the characteristics of both LSPs and diffractive states, enabling both enhanced local fields and narrow-linewidth excitations, in many respects providing the best advantages of both materials. Thus, by control of the periodicity and global symmetry of the lattice in addition to the material composition and shape of the constituent NPs, SLRs can be designed to simultaneously survive for up to 103 cycles while maintaining the electric field enhancements near the NP surface that have made the use of LSPs ubiquitous in nanoscience. Modern fabrication methods allow for square-centimeter-scale patches of two-dimensional arrays that are composed of approximately one trillion NPs, making them effectively infinite at the nanoscale. Because of these advances, it is now possible to experimentally realize SLRs with properties that approach those predicted by idealized theoretical models. In this Account, we introduce the fundamental theory of both SLRs and SLR-mediated lasing, where the latter is one of the most important applications of plasmonic SLRs that has emerged to date. The focus of this Account is on theoretical concepts for describing plasmonic SLRs and computational methods used for their study, but throughout we emphasize physical insights provided by the theory that aid in making applications.