This paper reviews the main properties and applications of nanomembrane-based plasmonic structures, including some results presented here for the first time. Artificial nanomembranes are a novel building block in micro- and nanosystems technologies. They represent quasi-two-dimensional (2D) freestanding structures thinner than 100 nm and with giant aspect ratios that often exceed 1,000,000. They may be fabricated as various quasi-2D metal-dielectric nanocomposites with tailorable properties; they are fully symmetric in an electromagnetic sense and support long-range surface plasmon polaritons. This makes nanomembranes a convenient platform for different plasmonic structures such as subwavelength plasmonic crystals and metamaterials and applications such as plasmon waveguides and ultrasensitive bio/chemical sensors. Among other advantages of nanomembrane plasmonics is the feasibility to fabricate flexible, transferable plasmonic guides applicable to different substrates and dynamically tunable through stretching. There are various approaches to multifunctionalization of nanomembranes for plasmonics, including the use of transparent conductive oxide nanoparticles, but also the incorporation of switchable ion channels. Since the natural counterpart of the artificial nanomembranes are cell membranes, the multifunctionalization of synthetic nanomembranes ensures the introduction of bionic principles into plasmonics, at the same time extending the toolbox of the available nanostructures, materials and functions.