Big time-series data have been generated in various applications including sensor networks, financial systems, online documents, medical information, web access records, social networking services, etc. How can we efficiently and effectively find typical patterns? How can we statistically summarize all the sequences, and achieve a meaningful segmentation? What are the major tools for forecasting and outlier detection? This paper summarizes our recent work, which includes: SpikeM that analyzes the rise and fall patterns of influence propagation in social networking services, TriMine for fast mining and forecasting of complex time-stamped events, AutoPlait for automatic mining of co-evolving multidimensional time sequences, EcoWeb as ecology-inspired nonlinear dynamical systems for pattern extraction from online activities, FUNNEL for automatic mining of spatially co-evolving epidemics, CompCube for non-linear mining of competing local activities, and RegimeCast for real-time forecasting of data streams.