In this article, we examine how thinking with affect theory offers fertility within higher education studies to see and do teaching and learning differently. For many educators in universities, the idea that teaching is a cognitive process of information transmission is still taken-for-granted. These beliefs are visible through the persistence of nomenclature such as 'content', predictable learning 'outcomes', and by the dominance of linear teaching aids (such as PowerPoint slides) across the sector internationally. An alternative conception of what teaching and learning is, and does, posits the classroom as a space of emergent relational connections in which learning is experienced as an affective force that constitutes being-in-the-world. To sketch shapes for understanding the affective encounters of teaching and learning, we think with the concept of "inconvenience" from the work of cultural theorist Lauren Berlant. We offer three illustrative examples of how teaching might be understood as an opportunity to surface, to welcome, and to problematise the inconvenience of others. Our argument is that an engagement with the affective in education can help us in understanding how power relations make themselves felt within the affective currents of educational encounters, as well as enabling educators to recraft their teaching in creative and meaningful ways. We conclude by contending that critical theories of affect can enhance educators' work towards fostering social justice in the classroom, as well as in moving closer to an enriched understanding of the discomfort and challenge of what it means to teach and to learn.