Hyperspectral imaging (HSI) is an emerging imaging modality for medical applications, especially in disease diagnosis and image-guided surgery. HSI acquires a three-dimensional dataset called hypercube, with two spatial dimensions and one spectral dimension. Spatially resolved spectral imaging obtained by HSI provides diagnostic information about the tissue physiology, morphology, and composition. This review paper presents an overview of the literature on medical hyperspectral imaging technology and its applications. The aim of the survey is threefold: an introduction for those new to the field, an overview for those working in the field, and a reference for those searching for literature on a specific application.