Different aspects of noise in X-ray computed tomography (XCT) for industrial purposes are examined. An overview of the most common noise metrics is given, together with a description of XCT noise influence quantities. We address the current state of the art in understanding the contribution of noise to XCT measurement uncertainty, giving a chronological view of the different attempts that have been made to account for the contribution from noise to XCT measurement uncertainty. We conclude that approaches to estimating the contribution of noise to XCT measurement uncertainty that account for not only noise, but also other factors that affect image quality (e.g., scattering, beam hardening and blurring) are preferable to approaches that only account for noise.