“Uncertainty” is the ongoing realization that we cannot predict the future, and “surprise” reminds us lest we forget. Despite the fact that uncertainty is an undeniable fact of everyday experiences, in particular when providing care to patients, it is ignored and under-evaluated scientifically. Understandably and appropriately, medical science seeks knowledge, certainty, and prediction; however, the fundamental truth of intrinsic irreducible uncertainty remains neglected. The principal hypothesis of this article is that greater acceptance and understanding of intrinsic uncertainty offers valuable insights towards improving the delivery and management of health care, as well as the performance of clinical and basic science research. This review highlights the ubiquitous presence and acceptance of irreducible uncertainty in diverse domains of science, defines and classifies uncertainty arising from this awareness, and explores the insights and implications of this understanding with regard to health-care practice, health-care management, physician-patient communication, basic science research, and clinical research. It offers specific recommendations in each area of focus that are proposed to stimulate deliberation and investigation.