As multi-dimensional data arrays, tensors play a central role in data science and machine learning. In this talk, I will discuss efficient tensor algorithms and their applications in data science. In the first part of the talk, I will introduce a stochastic mixed-precision method for large-scale tensor computations. By leveraging block sampling together with low-precision arithmetic, this approach significantly reduces both memory usage and computational cost for gradient evaluations, thereby accelerating tensor decomposition algorithms. Neural networks have grown rapidly in size in recent years, leading to substantial memory and computation costs that pose major challenges for training and deployment. In the second part of the talk, I will discuss how tensor methods and tensor decompositions can be used to compress large neural networks, thereby accelerating both training and inference.