Hyperspectral imaging, providing abundant spatial and spectral information simultaneously, has attracted a lot of interest in recent years. Unfortunately, due to the hardware limitations, the hyperspectral image (HSI) is vulnerable to various degradations, such noises (random noise, HSI denoising), blurs (Gaussian and uniform blur, HSI deblurring), and down-sampled (both spectral and spatial downsample, HSI super-resolution). Previous HSI restoration methods are designed for one specific task only. Besides, most of them start from the 1-D vector or 2-D matrix models and cannot fully exploit the structurally spectral-spatial correlation in 3-D HSI. To overcome these limitations, in this work, we propose a unified low-rank tensor recovery model for comprehensive HSI restoration tasks, in which non-local similarity between spectral-spatial cubic and spectral correlation are simultaneously captured by 3-order tensors. Further, to improve the capability and flexibility, we formulate it as a weighted low-rank tensor recovery (WLRTR) model by treating the singular values differently, and study its analytical solution. We also consider the exclusive stripe noise in HSI as the gross error by extending WLRTR to robust principal component analysis (WLRTR-RPCA). Extensive experiments demonstrate the proposed WLRTR models consistently outperform state-of-the-arts in typical low level viThis work was supported in part by the projects of the National Natural Science Foundation of China under Grants No. 61571207, 61433007 and 41501371. Yi Chang, Luxin Yan, Sheng Zhong and Zhijun Zhang Science and Technology on Multispectral Information Processing Laboratory, School of Automation, Huazhong University of Science and Technology, Wuhan, 430074, China. E-mail: yichang, yanluxin, zhongsheng, firstname.lastname@example.org Houzhang Fang National Laboratory of Radar Signal Processing, Xidian University, Xi’an, 710071, China E-mail: email@example.com sion HSI tasks, including denoising, destriping, deblurring and super-resolution.