International students undertaking a higher degree by research may experience a range of difficulties and challenges while studying in their host country. Some of these challenges, including language and cultural difficulties, limited peer relationships and challenges in forming relationships with supervisors, have been outlined in the literature but there is less research that has considered both the experiences of international students and supervisors together to provide a cohesive overview of the issues that international higher-degree-by-research students may face. Using a qualitative interview design, this research therefore sought to examine this issue within one faculty in a single university in Australia. International higher-degree-by-research students were found to be diverse in their expectations and desires of their new host country and university. Thus, it should not be assumed that all students will have similar priorities. The article provides some suggestions for universities when developing or refining their programmes to better support international higher-degree-by-research students in settling into their new country and programme of study.