Precision medicine promises better healthcare delivery by improving clinical practice. Using evidencebased substratification of patients, the objective is to achieve better prognosis, diagnosis, and treatment that will transform existing clinical pathways toward optimizing care for the specific needs of each patient. The wealth of today's healthcare data, often characterized as big data, provides invaluable resources toward new knowledge discovery that has the potential to advance precision medicine. The latter requires interdisciplinary efforts that will capitalize the information, know-how, and medical data of newly formed groups fusing different backgrounds and expertise. The objective of this paper is to provide insights with respect to the state-of-the-art research in precision medicine. More specifically, our goal is to highlight the fundamental challenges in emerging fields of radiomics and radiogenomics by reviewing the case studies of Cancer and Alzheimer's disease, describe the computational challenges from a big data analytics perspective, and discuss standardization and open data initiatives that will facilitate the adoption of precision medicine methods and practices.