A very important application of time series learning is online diagnosis, or monitoring, to detect and classify hazardous conditions in a physical system. Examples of crisis monitoring in the industrial, military, agricultural and environmental sciences are numerous. This paper first defines heterogeneous time series, those containing different types of embedded, statistical patterns. Next, it surveys basic techniques for acquiring several types of temporal models (using artificial neural networks and Bayesian networks). A new system for learning heterogeneous time series is then presented; it uses task decomposition and quantitative metrics to select techniques for each identifiable (and relevant) embedded subproblem. This solution is briefly compared to some mixture models for recombining specialized classifiers. The validation experiments use two large-scale applications, shipboard damage control automation and crop monitoring in precision agriculture. This paper concludes with a report on work in progress and some early positive learning results regarding these application domains.