Controversy is an inevitable aspect of our daily lives. Besides its deleterious aspects, it is also a constitutive ingredient of sustained cooperation in a society, of peaceful democracy as well. Its effectiveness on citizens can vary in ways ranging from shaping their beliefs, giving rise to fruitful conversations between parties, to openness to others who hold different identities, and cultural backgrounds. For that reason, it has been taken that bringing controversial topics into classrooms and schools will provide students and society with multifarious salutary tools as such to lead a flourishing life. By the same token, teaching controversial issues in schools have been justified on the basis that it brings out critical thinking, questioning skills and political participation of students. However, despite the valuableness of controversial issues, there is little attention has been paid to how controversial issues can be identified. However, there are some functional criteria for identifying controversial issues in the relevant field. In fact, the criteria put forward contain many discussions among themselves and against each other. This provides a rich resource for teachers who want to use controversial topics in education/classroom environment. These criteria include behavioral criterion, epistemic criterion, political criterion, and political authentic criterion. Therefore, this article brings to the fore the question "Which criteria should be deployed in selecting controversial issues?" and theoretically gives an indetail examination of criteria that have been proposed with respect to selecting controversial issues. Having drilled down each criterion's pros and cons deeply, as an epilogue, this article is to addresses which virtues teachers should aspire to cultivate in themselves.