Multiple-instance learning (MIL) is a recent machine-learning paradigm that is particularly well suited to medical image and video analysis (MIVA) tasks. Based solely on class labels assigned globally to images or videos, MIL algorithms learn to detect relevant patterns locally in images or videos. These patterns are then used for classification at a global level. Because supervision relies on global labels, manual segmentations are not needed to train MIL algorithms, unlike traditional single-instance learning (SIL) algorithms. Consequently, these solutions are attracting increasing interest from the MIVA community: since the term was coined by Dietterich et al. in 1997, 73 research papers about MIL have been published in the MIVA literature. This paper reviews the existing strategies for modeling MIVA tasks as MIL problems, recommends general-purpose MIL algorithms for each type of MIVA tasks, and discusses MIVA-specific MIL algorithms. Various experiments performed in medical image and video datasets are compiled in order to back up these discussions. This meta-analysis shows that, besides being more convenient than SIL solutions, MIL algorithms are also more accurate in many cases. In other words, MIL is the ideal solution for many MIVA tasks. Recent trends are discussed, and future directions are proposed for this emerging paradigm.