Multiple theories beyond the Standard Model predict the existence of heavy neutrinos, such as the type-I or type-III seesaw mechanisms that can explain the light neutrino masses, or left-right symmetric models that restore parity symmetry in weak interactions at a higher energy scale and predict right-handed counterparts to the weak gauge bosons. Searches for such heavy Majorana or Dirac neutrinos with the ATLAS detector, which can lead to boosted or displaced signatures, are presented using proton-proton data from the LHC at a center-of-mass energy of 13 TeV.