This article explores the potential of Computed Tomography (CT), micro- CT and nano-CT to provide three-dimensional radiographic images of textiles. It builds on the principles and practice of textile radiography presented at the ICOM-CC Hague meeting which aimed to establish radiography as a standard, nondestructive procedure for documentation and investigation of textiles and the planning of their conservation. Computed tomography is described and its benefits and drawbacks for understanding textiles are evaluated. Two case studies of multilayered archaeological textiles illustrate the application of CT in the investigation of complex textile objects and micro-CT is evaluated using two test objects of known construction and materials.