Explore the intricacies of low-rank tensor completion in this 32-minute lecture by Ming Yuan from Columbia University. Delve into the challenges associated with recovering low-rank tensors from partial observations, a task increasingly common yet complex due to the delicate nature of higher-order tensor decomposition. Examine several approaches to low-rank tensor completion, including matrix composition, multilinear ranks, and simple matrices. Gain insights into initialization techniques and compare two main approaches to solving this problem. This talk, part of the "Tensor Methods and Emerging Applications to the Physical and Data Sciences 2021" workshop at the Institute for Pure & Applied Mathematics (IPAM), UCLA, offers a comprehensive overview of recent investigations in this field.