Time series classification has been an active area of research in the data mining community for over a decade, and significant progress has been made in the tractability and accuracy of learning. However, virtually all work assumes a one-time training session in which labeled examples of all the concepts to be learned are provided. This assumption may be valid in a handful of situations, but it does not hold in most medical and scientific applications where we initially may have only the vaguest understanding of what concepts can be learned. Based on this observation, we propose a never-ending learning framework for time series in which an agent examines an unbounded stream of data and occasionally asks a teacher (which may be a human or an algorithm) for a label. We demonstrate the utility of our ideas with experiments in domains as diverse as medicine, entomology, wildlife monitoring, and human behavior analyses.