In 1976, Keith Dennis discovered an entirely novel technique for computing "K"-theory based on Hochschild homology. This was based around the existence of the Dennis trace map, a homomorphism from "K"-theory to Hochschild homology. While the Dennis trace map seemed to be successful for calculations of "K"-theory with finite coefficients, it was less successful for rational calculations. Goodwillie, motivated by his "calculus of functors", conjectured the existence of a theory intermediate to "K"-theory and Hochschild homology. He called this theory topological Hochschild homology because its ground ring should be the sphere spectrum (considered as a ring whose operations are defined only up to homotopy). In the mid-1980s, Bokstedt gave a definition of topological Hochschild homology that satisfied nearly all of Goodwillie's conjectural properties, and this made possible further computations of "K"-groups. Bokstedt's version of the Dennis trace map was a transformation of spectra . This transformation factored through the fixed points of a circle action on "THH", which suggested a relationship with cyclic homology. In the course of proving an algebraic "K"-theory analog of the Novikov conjecture, Bokstedt, Hsiang, and Madsen introduced topological cyclic homology, which bore the same relationship to topological Hochschild homology as cyclic homology did to Hochschild homology.