This article reports the findings of a research study on how significant having a foreign accent is for non-native English as a foreign language teachers and learners at university level. It points out the perceptions that teachers and students have about the most relevant issues in the teaching and learning processes. Data were collected by means of a questionnaire answered by thirty-two participants: eight Colombian teachers, eight foreign teachers, eight Colombian students, and eight foreign students. The findings show that although both teachers and students recognize the importance of having a native or native-like accent, they do not see this as the most relevant qualification to teach a language, nor the sole criterion positively affecting learning.