  This paper sketches the history of the Takagi function T and surveys known
properties of T, including its nowhere-differentiability, modulus of
continuity, graphical properties and level sets. Several generalizations of the
Takagi function, in as far as they are based on the "tent map", are also
discussed. The final section reviews a number of applications of the Takagi
function to various areas of mathematics, including number theory,
combinatorics and classical real analysis.
