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-80s, 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.