Asymptotic dimension

The asymptotic dimension theory was founded by Gromov [M. Gromov, Asymptotic invariants of infinite groups, in: Geometric Group Theory, vol. 2, Sussex, 1991, in: London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295] in the early 90s. In this paper we give a survey of its recent history where we emphasize two of its features: an analogy with the dimension theory of compact metric spaces and applications to the theory of discrete groups.