The view of the urban environment as an extended nonlinear system introduces new concepts, motivates new questions, and suggests new methodologies in the study of urban dynamics. A review of recent results on interface dynamics in nonequilibrium physical systems is presented, and possible implications on the urban environment are discussed. It is suggested that the growth modes of specific urban zones (e.g. residential, commercial, or industrial) and the factors affecting them can be studied using mathematical models that capture two generic interface instabilities.