After receiving his M.D. from Northwestern University, Dr. Wolf completed Urology residency at UCSF and then an Endourology / Laparoscopy Fellowship with Ralph Clayman. He joined the University of Michigan in 1996, and over the ensuing 20 years he served as the Director of the Division of Endourology, the Director of the Endourology / Laparoscopy Fellowship, and the Associate Urology Department Chair for Surgical Services. In 2016 he joined the Department of Surgery and Perioperative Care at Dell Medical School of the University of Texas at Austin, where he serves as the Associate Chair for Clinical Integration and Operations, Executive Associate Chair, and Chief of the Division of Surgical Specialties.

Dr. Wolf has served on the Boards of Directors of the Michigan Urologic Society, the Endourological Society, the Society of Academic Urologists and the Texas Urological Society. He chaired the American Urological Association (AUA) Practice Guidelines Committee and was the inaugural chair of the AUA Science & Quality Council. At the University of Michigan, Dr. Wolf received the Silver Cystoscope Award for Urology Residency Teaching Excellence three times (1999, 2002 and 2005). He was appointed the inaugural David A. Bloom Professor of Urology in 2006. The Department of Urology awarded him the Faculty Service Award in 2011 and the Outstanding Achievement Award in 2012. He was inducted into the League of Educational Excellence of the University of Michigan Medical School in 2015, and that year he also received the inaugural Program Director's Award from the Endourological Society and was the Malcolm Coptcoat Lecturer for The British Association of Urologic Surgeons. In 2010, Dr. Wolf was elected to the American Association of Genitourinary Surgeons. In 2018, he started a 6-year term as a Trustee of the American Board of Urology; in 2022 he assumed the role of President-Elect and will become President in 2023. Dr. Wolf received a Distinguished Service Award from the AUA in 2019.

An author of over 325 peer-reviewed articles and videos, and over 175 invited publications, Dr. Wolf has served on the editorial boards of 12 journals. His scholarly work has been recognized by awards and/or research grants from the American Foundation for Urologic Disease, the Department of Veterans Affairs, the Endourological Society, the American Society of Transplant Surgeons, and the AUA and 2 of its Sections.