Surface plasmon polaritons and their localized counterparts, surface plasmons, are widely used at visible and near-infrared (near-IR) frequencies to confine, enhance, and manipulate light on the subwavelength scale. At these frequencies, surface plasmons serve as enabling mechanisms for future on-chip communications architectures, high-performance sensors, and high-resolution imaging and lithography systems. Successful implementation of plasmonics-inspired solutions at longer wavelengths, in the mid-infrared (mid-IR) frequency range, would benefit a number of highly important technologies in health- and defense-related fields that include trace-gas detection, heat-signature sensing, mimicking, and cloaking, and source and detector development. However, the body of knowledge of visible/near-IR frequency plasmonics cannot be easily transferred to the mid-IR due to the fundamentally different material response of metals in these two frequency ranges. Therefore, mid-IR plasmonic architectures for subwavelength light manipulation require both new materials and new geometries. In this work we attempt to provide a comprehensive review of recent approaches to realize nano-scale plasmonic devices and structures operating at mid-IR wavelengths. We first discuss the motivation for the development of the field of mid-IR plasmonics and the fundamental differences between plasmonics in the mid-IR and at shorter wavelengths. We then discuss early plasmonics work in the mid-IR using traditional plasmonic metals, illuminating both the impressive results of this work, as well as the challenges arising from the very different behavior of metals in the mid-IR, when compared to shorter wavelengths. Finally, we discuss the potential of new classes of mid-IR plasmonic materials, capable of mimicking the behavior of traditional metals at shorter wavelengths, and allowing for true subwavelength, and ultimately, nano-scale confinement at long wavelengths.