This dissertation presents searches for partners of the top quark based on 36 fb-1 pp-collision data recorded at a centre-of-mass energy of 13 TeV with the ATLAS experiment at the LHC. Top quark partner particles are motivated in many models of physics beyond the Standard Model. The two scenarios considered are a vector-like top quarks, as well as a supersymmetric top squark. For each of these two models, one analysis is presented. The background processes are normalised in dedicated control regions. No excess above the Standard Model expectation is observed and 95% CL limits on the production cross-sections are derived. The observed (expected) lower limit on the vector-like top quark mass is 1.16 TeV (1.17 TeV) for decays into a Z boson and a top quark. For pair-produced top squarks decaying into top quarks, top squark masses up to 940 GeV are excluded (1020 GeV expected).