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This report presents a comprehensive collection of searches for new physics performed by the ATLAS Collaboration during the Run~2 period of data taking at the Large Hadron Collider, from 2015 to 2018, corresponding to about 140~$$^{-1}$$ of $$\sqrt{s}=13$$~TeV proton--proton collision data. These searches cover a variety of beyond-the-standard model topics such as dark matter candidates, new vector bosons, hidden-sector particles, leptoquarks, or vector-like quarks, among others. Searches for supersymmetric particles or extended Higgs sectors are explicitly excluded as these are the subject of separate reports by the Collaboration. For each topic, the most relevant searches are described, focusing on their importance and sensitivity and, when appropriate, highlighting the experimental techniques employed. In addition to the description of each analysis, complementary searches are compared, and the overall sensitivity of the ATLAS experiment to each type of new physics is discussed. Summary plots and statistical combinations of multiple searches are included whenever possible.