We assess economics research and teaching frameworks in the United States by examining how knowledge is produced and ranked, the flaws and strengths of heterodox economic theory; and how students are trained, especially for careers in economic policy. We challenge the meaning of established terminology such as 'heterodoxy' and 'mainstream' by investigating their utility as a marker and to illuminate major barriers to the successful adoption of alternative economic theories in academia and the public discourse. Based on interviews with experienced economists working with heterodox paradigms in both mainstream and heterodox institutions, we identify three barriers 1) Neoclassical hegemony, 2) Weakness of heterodox theory, and 3) Pedagogy and training in economics.