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Plasmons have been widely studied over the past several decades because of their ability to strongly absorb light and localize its electric field on the nanoscale, leading to applications in spectroscopy, biosensing, and solar energy storage. In a classical electrodynamics framework, a plasmon is defined as a collective, coherent oscillation of the conduction electrons of the material. In recent years, it has been shown experimentally that noble metal nanoclusters as small as a few nm can support plasmons. This work has led to numerous attempts to identify plasmons from a quantum mechanical perspective, including many overlapping and sometimes conflicting criteria for plasmons. Here, we shed light on the definitions of plasmons. We start with a brief overview of the well-established classical electrodynamics definition of a plasmon. We then turn to the experimental features used to determine whether a particular system is plasmonic, connecting the experimental results to the corresponding features of the classical electrodynamics description. The core of this article explains the many quantum mechanical criteria for plasmons. We explore the common features that these criteria share and explain how these features relate to the classical electrodynamics and experimental definitions. This comparison shows where more work is needed to expand and refine the quantum mechanical definitions of plasmons.