The completion of the Human Genome Project in 2003 has led to significant advances in patient care in medicine, particularly in diagnosing and managing genetic diseases and cancer. In the realm of genetic diseases, approximately 15% of critically ill infants born in the U.S.A. are diagnosed with genetic disorders, which comprise a significant cause of mortality in neonatal and pediatric intensive care units. The introduction of rapid whole-genome sequencing (rWGS) as a first-tier test in critically ill children with suspected, undiagnosed genetic diseases is a breakthrough in the diagnosis and subsequent clinical management of such infants and older children in intensive care units. Rapid genome sequencing is currently being used clinically in the USA, the UK, the Netherlands, Sweden, and Australia, among other countries. This review is intended for students and clinical practitioners, including non-experts in genetics, for whom it provides a historical background and a chronological review of the relevant published literature for the progression of pediatric diagnostic genomic sequencing leading to the development of pediatric rWGS in critically ill infants and older children with suspected but undiagnosed genetic diseases. Factors that will help to develop rWGS as a clinical test in critically ill infants and the limitations are briefly discussed, including an evaluation of the clinical utility and accessibility of genetic testing, education for parents and providers, cost-effectiveness, ethical challenges, consent issues, secondary findings, data privacy concerns, false-positive and false-negative results, challenges in variant interpretation, costs and reimbursement, the limited availability of genetic counselors, and the development of evidence-based guidelines, which would all need to be addressed to facilitate the implementation of pediatric genomic sequencing in an effective widespread manner in the era of precision medicine.