Top quark condensation

Top quark condensation, in particular the minimal framework where the neutral Higgs scalar is (predominantly) an effective ¯ tt condensate of the stan- dard model, is reviewed. Computational approaches are compared and sim- ilarities, differences and deficiencies pointed out. Extensions of the minimal framework, including scenarios with two composite Higgs doublets, additional neutrino condensates, andcondensation arising from four-fermion interac- tions with enlarged symmetries, are described. Possible renormalizable mod- els of underlying physics potentially responsible for the condensation, includ- ing 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.