Tensors are multi-way arrays that can generalize matrices to higher orders. Tensor modeling and processing are ubiquitous in modern data analysis and machine learning, as they capture inherent multi-linear structures within the data. For example, tensors are used for modeling multi-relational graphs, multi-spectral images/videos, wireless spectrum utilization maps, and even the parameters of neural networks. While matrix analysis has been thoroughly studied for a very long time, there is still much room (and need) for research in tensor analysis. Primarily funded by NSF and AFOSR, in this research direction we develop new methods for dynamic and robust analysis of tensor data.