Searches for new physics in the top-quark sector using data from proton-antiproton collisions at the Fermilab Tevatron are discussed. The large data sets collected by the D0 and CDF experiments allow for precision measurements of the standard model (SM) top-quark production rates and top quark properties so that deviations from the SM expectations can be interpreted as signs of new physics. The presented analyses exploit the fact that the new physics would reveal itself in final states that are similar or identical to those of SM top-antitop production.