Top-quark condensation, in particular the minimal framework in which the neutral Higgs scalar is (predominantly) an effective $\overline{t}t$ condensate of the standard model, is reviewed. Computational approaches are compared and similarities, differences, and deficiencies pointed out. Extensions of the minimal framework, including scenarios with two composite Higgs doublets, additional neutrino condensates, and $\overline{t}t$ condensation arising from four-fermion interactions with enlarged symmetries, are described. Possible renormalizable models of underlying physics potentially responsible for the condensation, including topcolor-assisted technicolor frameworks, are discussed. Phenomenological implications of top condensate models are outlined. Outstanding theoretical issues and problems for future investigation are pointed out. Progress in the field after this article was accepted has been briefly covered in a Note added at the end.

DOI:https://doi.org/10.1103/RevModPhys.71.513