Various theories beyond the Standard Model predict unique signatures which are difficult to reconstruct and for which estimating the background rates is also a challenge. Signatures from displaced decays anywhere from the inner detector to the muon spectrometer, as well as those of new particles with fractional or multiple value of the charge of the electron or high-mass stable charged particles are all examples of experimentally demanding signatures. This review focuses on the most recent results using LHC pp collision data at 13 TeV collected by the ATLAS detector.