Critical thinking is often considered to involve a set of skills required by graduates of higher educational institutions in the UK. However, the conceptualisation of critical thinking by university tutors varies across disciplines and is not always particularly clear. In a UK higher educational context where proportionally increasing numbers of postgraduate students are international, often from educational traditions where critical thinking is less of a priority, it is important to compare international student understanding of critical thinking with that of postgraduate course tutors. This thesis aimed to compare the conceptualisations of critical thinking skills by postgraduate students and tutors, and gauge how these skills are connected to academic writing at a UK Russell Group university. To do this, a mixed methods approach was adopted involving three main stages: a student questionnaire, focus groups and interviews with students, and interviews with tutors. The questionnaire asked 235 students to rate the importance of different statements describing features of academic writing based on aspects of written argumentation and cognitive skills. Results show that clear argumentation was ranked highly, alongside the skills of comparing and evaluating content. Analysis of the findings from the focus groups and interviews with students and tutors resulted in three main themes: that critical reading was an essential component of critical writing; that clear argumentation and voice are important features of critical academic writing, and that there was what appeared to be a phase in the process of academic writing which I have labelled as a '(re)construction' phase. For students, this involved the importance of comparing and evaluating different viewpoints and perspectives, while for tutors it involved the need for academic writers to make connections between theory, evidence and practice. A final question looked at what were perceived to be the most effective approaches to teaching and learning critical thinking at a postgraduate master's level. Both students and tutors agreed that an 'infusion' approach to teaching critical thinking could be most effective. This involves the teaching of critical thinking skills explicitly within specific disciplines. Although a separate generic course on critical thinking was less popular, the role of current research methods courses and (to a limited extent) study skills courses were key elements involved in the second most popular response, which involved a mixture of different approaches. Pedagogical implications of these findings include the need to focus on the role of tutors in teaching explicitly what it means to be critical within a discipline, and the role that research methods courses can have in reinforcing more generic aspects of critical thinking.