A review of theory and experiment of two-dimensional magnetic phase transit
ions is presented. I consider principal systems from the point of view of t
he general theory of phase transitions and the corresponding statistical mo
dels. The topological point of view of the phase transitions is analysed. C
onformal groups and its consequences in two dimensions are reviewed. Some u
nsolved problems are discussed. (C) 1999 Elsevier Science B.V. All rights r
eserved.