Metallic nanostructures have received great attention due to their ability to generate surface plasmon resonances, which are collective oscillations of conduction electrons of a material excited by an electromagnetic wave. Plasmonic metal nanostructures are able to localize and manipulate the light at the nanoscale and, therefore, are attractive building blocks for various emerging applications. In particular, hollow nanostructures are promising plasmonic materials as cavities are known to have better plasmonic properties than their solid counterparts thanks to the plasmon hybridization mechanism. The hybridization of the plasmons results in the enhancement of the plasmon fields along with more homogeneous distribution as well as the reduction of localized surface plasmon resonance (LSPR) quenching due to absorption. In this review, we summarize the efforts on the synthesis of hollow metal nanostructures with an emphasis on the galvanic replacement reaction. In the second part of this review, we discuss the advancements on the characterization of plasmonic properties of hollow nanostructures, covering the single nanoparticle experiments, nanoscale characterization via electron energy-loss spectroscopy and modeling and simulation studies. Examples of the applications, i.e. sensing, surface enhanced Raman spectroscopy, photothermal ablation therapy of cancer, drug delivery or catalysis among others, where hollow nanostructures perform better than their solid counterparts, are also evaluated.