The American Association of Physicists in Medicine (AAPM) and the Society of Nuclear Medicine and Molecular Imaging (SNMMI) recognized the need for a review of the current state of nuclear medicine physics training and the need to explore pathways for improving nuclear medicine physics training opportunities. For these reasons, the two organizations formed a joint AAPM/SNMMI Ad Hoc Task Force on Nuclear Medicine Physics Training. The mission of this task force was to assemble a representative group of stakeholders to: Estimate the demand for board-certified nuclear medicine physicists in the next 5-10 years, Identify the critical issues related to supplying an adequate number of physicists who have received the appropriate level of training in nuclear medicine physics, and Identify approaches that may be considered to facilitate the training of nuclear medicine physicists. As a result, a task force was appointed and chaired by an active member of both organizations that included representation from the AAPM, SNMMI, the American Board of Radiology (ABR), the American Board of Science in Nuclear Medicine (ABSNM), and the Commission for the Accreditation of Medical Physics Educational Programs (CAMPEP). The Task Force first met at the AAPM Annual Meeting in Charlotte in July 2012 and has met regularly face-to-face, online, and by conference calls. This manuscript reports the findings of the Task Force, as well as recommendations to achieve the stated mission. PACS number: 01.40.G.