The purpose of this study is to provide an account of preservice elementary mathematics teachers' understandings about irrational numbers. Three dimensions of preservice mathematics teachers' understandings are examined: defining rational and irrational numbers, placing rational and irrational numbers on the number line, and operations with rational and irrational numbers. The study was conducted with 80 first- and fourth-year preservice elementary mathematics teachers with the use of an open-ended test consisting of 10 questions prepared through a literature review. The findings showed that participants hold misunderstandings about the definitions of irrational numbers, operations between rational and irrational number sets, and their relationship on the number line. Explanations used by the majority of participants were based on representations and intuitions. (Contains 5 tables and 1 figure.)