Synchrotron-radiation computed laminography (SRCL) was developed as a nondestructive three-dimensional (3D) imaging technique for flat and laterally extended objects. Complementing the established method of computed tomography, SRCL is based on the inclination of the tomographic axis with respect to the incident x-ray beam by a defined angle. Its ability for 3D imaging of regions of interest in flat specimens was demonstrated in various fields of investigation, e.g. in nondestructive testing, material science and life sciences. We introduce the principles of the method and report on the latest developments of SRCL. The experimental setups at the ESRF beamlines ID19 and ID22NI are dedicated to 3D micro-and nano-scale imaging, respectively, utilising different contrast modes including absorption, phase contrast and fluorescence. Selected examples from materials science outline the potential of the method for an unparalleled nondestructive 3D characterisation of flat specimens.