We investigate some misconceptions concerning the cardinality of infinite sets. Students from three different groups were asked to complete a short questionnaire which contained questions designed to give insight into students’ concept images of infinity, cardinality and the comparison of infinite sets. The study highlighted some of the conceptions of students associated with finite, countable and uncountable infinite sets. These different conceptions and misconceptions might arise from: the meaning of words in everyday language; the incorrect use of properties which are true for some situations but not for all; the misuse of the bijection criterion; the different presentations of sets; or the idea of infinity as a number.