The quality of wines is usually evaluated by a sensory panel formed of trained experts or traditional chemical analysis. Over the last few decades, electronic noses (e-noses) and electronic tongues have been developed to determine the quality of foods and beverages. They consist of arrays of sensors with cross-sensitivity, combined with pattern recognition software, which provide a fingerprint of the samples that can be used to discriminate or classify the samples. This holistic approach is inspired by the method used in mammals to recognize food through their senses. They have been widely applied to the analysis of wines, including quality control, aging control, or the detection of fraudulence, among others. In this paper, the current status of research and development in the field of e-noses and tongues applied to the analysis of wines is reviewed. Their potential applications in the wine industry are described. The review ends with a final comment about expected future developments.