Sampling plays a central role in recovering low-rank structures from incomplete data. In this talk, I will present a unified framework of cross-concentrated sampling (CCS) and its tensor analog (t-CCS), which bridges the gap between unbiased sampling and CUR sampling. First, in the matrix setting, we consider a rank-r matrix and introduce a sampling scheme in which we select subsets of rows and columns and then sample within these “cross-concentrated” submatrices — thereby interpolating between uniform entry-sampling and full CUR sampling. We establish sufficient conditions (under incoherence) guaranteeing exact recovery via a tailored non-convex iterative CUR-completion algorithm (ICURC). Second, broadening to third-order tensors, we extend the CCS concept to the tubal-rank tensor framework: selecting lateral and horizontal subtensors of a low-tubal-rank tensor, sampling within them, and developing a non-convex solver (ITCURTC) with provable guarantees. Notably, we derive explicit constants in the sufficient sampling condition, and demonstrate the empirical advantages of t-CCS over classical Bernoulli or full t-CUR sampling in real datasets. The talk will highlight the underlying mathematical principles, algorithmic developments, and numerical validation, illustrating how flexible sampling models provide a unified foundation for matrix and tensor recovery.