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Simple Summary: Recently, radiogenomics has played a significant role and offered a new understanding of cancer's biology and behavior in response to standard therapy. It also provides a more precise prognosis, investigation, and analysis of the patient's cancer. Over the years, Artificial Intelligence (AI) has provided a significant strength in radiogenomics. In this paper, we offer computational and oncological prospects of the role of AI in radiogenomics, as well as its offers, achievements, opportunities, and limitations in the current clinical practices. Radiogenomics, a combination of "Radiomics" and "Genomics," using Artificial Intelligence (AI) has recently emerged as the state-of-the-art science in precision medicine, especially in oncology care. Radiogenomics syndicates large-scale quantifiable data extracted from radiological medical images enveloped with personalized genomic phenotypes. It fabricates a prediction model through various AI methods to stratify the risk of patients, monitor therapeutic approaches, and assess clinical outcomes. It has recently shown tremendous achievements in prognosis, treatment planning, survival prediction, heterogeneity analysis, reoccurrence, and progression-free survival for human cancer study. Although AI has shown immense performance in oncology care in various clinical aspects, it has several challenges and limitations. The proposed review provides an overview of radiogenomics with the viewpoints on the role of AI in terms of its promises for computational as well as oncological aspects and offers achievements and opportunities in the era of precision medicine. The review also presents various recommendations to diminish these obstacles. [ABSTRACT FROM AUTHOR]