Using state-of-the-art many-body calculations based on the `GW plus cumulant' approach, we show that electron-plasmon interactions lead to the emergence of plasmonic polaron bands in the band structures of common semiconductors. Using silicon and group IV transition metal dichalcogenide monolayers (AX2 with A=Mo,W and X=S,Se) as prototypical examples, we demonstrate that these new bands are a general feature of systems characterized by well defined plasmon resonances. We find that the energy vs. momentum dispersion relations of these plasmonic structures closely follow the standard valence bands, although they appear broadened and blueshifted by the plasmon energy. Based on our results we identify general criteria for observing plasmonic polaron bands in the angle-resolved photoelectron spectra of solids. ; Comment: 5 pages, 3 figures