Background: Critical thinking is one of the very highest orders of cognitive abilities and a key competency in higher education. Asking questions is an important component of rich learning experiences, structurally embedded in the operations of critical thinking. Our clear sense is that critical thinking and, within that, critical questioning, is heavily context dependent, in the sense that is applied, used by critical learners in a contextualised way. Purpose: Our research deals with enhancing science undergraduates' critical questioning. We are interested in understanding and describing the nature and development of students' critical questioning. The purpose is to conceptualise critical questioning as a competency, into three domains--knowledge, skills and attitudes/dispositions. We have no interest in a taxonomic category of context-free question-types called "critical questions". In contrast, our view is that 'being a critical questioner' trades heavily on context. Sources of evidence: Four cases are considered as illuminative of the dimensions of science undergraduates' critical questioning. Data were collected in natural learning environments through non-participant observation, audio-taping teacher-students interactions and semi-structured interviews. Students' written material resulting from diverse learning tasks was also collected. Main argument: Our supposition is that one vehicle for achieving university students as critical thinkers is to enable them not just to ask critical questions, but to be critical questioners. We relate critical questioning to three domains: (1) context, (2) competency and (3) delivery, and propose a model based on illuminating examples of the in-classroom action. Conclusions: The dimensions of the competency-context-delivery model provide a framework for describing successful student critical questioning, showing that students' capacity to be critical can be developed. It is possible, in our view, to generate critical questioners by means of promoting a true spirit of critical inquiry. The model also gives important insights into the design of teaching, learning and assessment contexts, where critical questioning could be promoted.