3D seismic data reconstruction is typically regarded as an ill-posed inverse problemInverse problem, which requires the introduction of additional constraints to ensure accurate recovery. A widely adopted approach in this area is to apply rank-based techniques to derive the most efficient low-rank representation of a given Hankel matrix. However, this approach faces the issue that low-rank approximations may disrupt the inherent Hankel structureHankel structure, thereby impacting the accuracy of the recovery process. This chapter introduces a new approach: the structured low-tubal-rank tensor completion (STC) method, which integrates the Hankel structure with a low-tubal-rank regularization to improve recovery performance. Nevertheless, existing methods typically rely on element-wise sampling assumptions, making the solution to STC challenging, as Hankel constraints cannot be directly translated into linear tensor equations. To overcome this issue, we propose a novel tubal sampling approach that better captures the sampling pattern of missing traces. This technique enables us to establish a connection between tensor completionTensor completion and matrix completion. This connection provides two effective pathways for solving STC: first, by combining tensor and matrix completion, the STC problem can be transformed into a matrix completion problem by randomly sampling from each frontal slice in the Fourier domain, improving computational efficiency; second, this framework allows for the development of flexible tensor models under varying noise conditions, thus meeting the needs of data reconstruction in noisy environments. Furthermore, we utilize an alternating optimization strategy along with the alternating direction method of multipliers (ADMM) to solve the STC framework, which improves the stability and convergence of the solution process. Experimental validation on both synthetic and real seismic data demonstrates the effectiveness of the STC framework in improving seismic data recovery accuracy.