As plasmonic materials transition from three-dimensional to two-dimensional (2D) form, unique optical and electronic phenomena arise that are unattainable in bulk materials and conventional thin films. Exceptional sensitivity to external perturbations, including electrical biasing and optical excitation as well as quantum effects, are expected to emerge, as has been demonstrated in graphene. Similarly, metallic or plasmonic films with thicknesses down to a few monolayers, called transdimensional materials (TDMs), are predicted to exhibit remarkably strong tunability of their optical response. The unique properties of 2D materials and TDMs have established them as promising platforms for dynamic nanophotonic devices. While novel 2D materials have been widely explored for nanophotonic devices, until recently, there have been minimal studies on the evolution of the optical properties of plasmonic TDMs. In this article, we highlight progress in exploring the thickness-dependent optical response of plasmonic materials as they approach the 2D regime. Experimental and theoretical investigations of the plasmonic properties of 2D materials, such as graphene and tungsten diselenide, TDMs, and plasmonic thin films, are discussed, with a focus on prospects for their utilization in dynamically tunable flat optical devices or metasurfaces.