Abstract: Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. Rapid developments in high-throughput technologies have made multiway data readily available in daily lives. Tensor provides a generalized data structure in many learning procedures. Methods built on tensors provide powerful tools to capture complex structures that lower-order methods fail to exploit. However, the empirical success has uncovered a myriad of new and pressing challenges. In this talk, I will discuss some recent advances and challenges in high-dimensional tensor data algorithms. Potentials of these methods are illustrated through applications to Human Connectome Project (HCP) and Genotype-Tissue Expression (GTEx) datasets.