In the field of cancer genomics, the broad availability of genetic information offered by next-generation sequencing technologies and rapid growth in biomedical publication has led to the advent of the big-data era. Integration of artificial intelligence (AI) approaches such as machine learning, deep learning, and natural language processing (NLP) to tackle the challenges of scalability and high dimensionality of data and to transform big data into clinically actionable knowledge is expanding and becoming the foundation of precision medicine. In this paper, we review the current status and future directions of AI application in cancer genomics within the context of workflows to integrate genomic analysis for precision cancer care. The existing solutions of AI and their limitations in cancer genetic testing and diagnostics such as variant calling and interpretation are critically analyzed. Publicly available tools or algorithms for key NLP technologies in the literature mining for evidence-based clinical recommendations are reviewed and compared. In addition, the present paper highlights the challenges to AI adoption in digital healthcare with regard to data requirements, algorithmic transparency, reproducibility, and real-world assessment, and discusses the importance of preparing patients and physicians for modern digitized healthcare. We believe that AI will remain the main driver to healthcare transformation toward precision medicine, yet the unprecedented challenges posed should be addressed to ensure safety and beneficial impact to healthcare.