High-resolution and ultra-high-resolution X-ray computed tomography are rapid, non-destructive and extremely powerful techniques for three-dimensional examination and measurement of a great variety of geological materials and specimens with sizes from several millimetres to several decimetres. A review of recent applications in petrology, meteoritics and palaeontology, which utilized an instrument optimized for geological studies (HighResolution X-ray Computed Tomography Facility of the University of Texas at Austin), documents an abundance of novel scientific results and illuminates the potential for still broader application of these techniques in the earth sciences.Many earth science investigations require examination or measurement of the internal features of specimens in three dimensions, tasks to which X-ray computed tomography (CT) is well-suited. A variety of different X-ray CT instruments and techniques are available. The scale of the object to be studied and the spatial resolution required in the images commonly dictate which is employed (Table 1). High-resolution X-ray CT (HRXCT) and ultra-high-resolution X-ray CT (UHRXCT) are techniques suitable for studying objects with dimensions from a few millimetres to a few decimetres. Into this range of scales falls a wide variety of intriguing geological problems. This paper provides a selective review of recent HRXCT and UHRXCT work done at the University of Texas at Austin, in the form of very brief synopses of individual projects with references to the published literature for more complete exposition. Our purpose is to stimulate further exploitation of these techniques in the earth sciences by providing an overview of the broad range of geological questions that can be productively addressed using this rapid, non-destructive, visually powerful and fully digital tool.