High-entropy alloys (HEAs) are a recently opened research area in materials science and condensed matter physics. Although 3d-metal-based HEAs have already been the subject of many investigations, studies of HEA superconductors, which tend to be based on 4d metals, are relatively fewer. Here we provide a short update of the progress made in studies of superconducting HEAs. We aim to summarize their current status and describe some of the key factors that appear to influence their superconducting transition temperatures and properties, including crystal structure, atomic makeup, valence electron count, molar volume, and mixing entropy. Many opportunities and challenges remain for expanding our knowledge of HEA superconductors, finding new types of HEA superconductors, and their potential for applications; these are also briefly discussed.