Disclosed are a polymer, a polymer electrolyte and a use of the polymer or polymer electrolyte. The polymer has, as a structural unit, a phenylene group in which two or three hydrogen atoms are substituted with groups represented by formula (A), and is insoluble in water. (In formula (A), A1 represents a group represented by formula (1a), formula (1b) or formula (1c); and the two or three A1's may be the same as or different from each other.) (In formulae (1a)-(1c), R10 and R11 independently represent a hydrogen atom, an alkyl group having 1-20 carbon atoms or an aryl group having 6-20 carbon atoms; R12 represents a hydrogen atom, an alkyl group having 1-20 carbon atoms or an aryl group having 6-20 carbon atoms; M represents a metal ion or an ammonium ion; and when M is a divalent or higher-valent metal ion, M may also be bonded with another substituent.)