Performing arts teachers, in diverse regions of the world, recognise that globalisation has indelibly influenced how the arts are valued, practiced and taught (Rowe, Martin, Buck, et al., 2018). As illustrated by three key United Nations Education, Science and Culture Organisation (UNESCO) policies on arts and culture in the 21st century (UNESCO, 2003, 2006, 2011), global mandates can present contrasting imperatives, prompting shifts within regional, national and institutional strategies. So how do tertiary arts educators respond to shifts in global policies? After a brief historical analysis of three UNESCO strategic documents associated with arts education, this article considers how the contrasts within these strategies have presented challenging learning moments for arts educationalists. 'Threshold concept' theory is presented as a means of framing such learning challenges, to highlight the professional development needs of designers of tertiary curricula. Critically reflecting on the author's experiences of codesigning tertiary degree programmes in New Zealand, China and Fiji, this article identifies key conceptual thresholds that can challenge tertiary educators when seeking to align institutional teaching practices with contemporary global policies on arts education.