  Maximal antipodal sets of Riemannian manifolds were introduced by the author
and T. Nagano in [Un invariant g\'eom\'etrique riemannien, C. R. Acad. Sci.
Paris S\'er. I Math. 295 (1982), no. 5, 389--391]. Since then maximal antipodal
sets have been studied by many mathematicians and they shown that maximal
antipodal sets are related to several important areas in mathematics. The main
purpose of this paper is thus to present a comprehensive survey on geometry and
topology of maximal antipodal sets and also on their applications to several
related topics.
