  This survey of topological cyclic homology is a chapter in the Handbook on
Homotopy Theory. We give a brief introduction to topological cyclic homology
and the cyclotomic trace map following Nikolaus-Scholze, followed by a proof of
B\"okstedt periodicity that closely resembles B\"okstedt's original unpublished
proof. We explain the extension of B\"{o}kstedt periodicity by
Bhatt-Morrow-Scholze from perfect fields to perfectoid rings and use this to
give a purely p-adic proof of Bott periodicity. Finally, we evaluate the
cofiber of the assembly map in p-adic topological cyclic homology for the
cyclic group of order p and a perfectoid ring of coefficients.
