Mollapour completed his postdoctoral research at the University of Sheffield and in 2006 he received the Federation of European Societies (FEBS) fellowship.
He joined the laboratory of Dr Len Neckers in Urological Oncology Branch, (Chief Dr. W. Marston Linehan), at the National Cancer Institute as a research fellow in 2007.
In 2013 he joined the Department of Urology at the Upstate Medical University as an Assistant Professor. He became the Director of the Kidney Cancer Program within the same department in 2015.
In 2018 he became the Professor of Urology and Adjunct Professor of Biochemistry and Molecular Biology at SUNY Upstate Medical University. He was also named the Vice Chair for Translational Research for the Department of Urology in the same year. In 2023, Mollapour was elected the president-elect for the Cell Stress Society International; his term at president will begin in 2025. Mollapour’s h-index is 45, based on 7,751 citations.