This article reviews questions that non-native (NNEST) and native speaker (NEST) teachers, working in different contexts, have about pronunciation teaching. It draws on theory, research, and practice to answer those questions as far as possible. The data was collected across two projects that investigated teachers' cognitions: their knowledge, beliefs, attitudes, and practices. The first project involved semi-structured interviews with 28 NNESTs in Uruguay while the second was set in New Zealand and involved questionnaires (N=83), semistructured interviews (N=19) and classroom observations (N=6). The 19 New Zealand interviews involved 11 with New Zealand English native (L1) speakers, six with Inner Circle variety of English L1 speakers, one Outer Circle bilingual, and one Expanding Circle bilingual speaker. While a number of results from these studies have already been reported (Couper, 2016a, 2016b, 2017, 2019), this article revisits the data in order to isolate questions and issues, and compare them across the two contexts. The data from Uruguay reveal insights into NNESTs' perspectives while the data from New Zealand provide perspectives from those teaching Asian L1 students. Questions relate to: (1) the learner; (2) what to teach; (3) how to teach; (4) dealing with curriculum, textbook, and time issues; and (5) teacher's pronunciation ability and knowledge of phonetics and phonology. There are some differences between the groups, such as NNESTs lacking confidence in their own pronunciation and NESTs lacking knowledge of phonetics and phonology. However, there are more similarities, with many questions not being specific to either context. These involve pedagogic knowledge and issues around priorities, setting goals, and space for pronunciation teaching. The questions and issues are addressed in terms of theories and what is known from the increasing body of research into pronunciation teaching. Practical examples of how this knowledge can be applied in the classroom are also suggested.