In nondestructive testing (NDT) of microelectronic components many applications using X-ray radiography are well established. This method is based on the attenuation of radiation intensities of x-rays transmitting an object. Computer tomography (CT), however, is a visualization method which is based on reconstructing three-dimensional models from several two-dimensional X-ray projections of the object. It is only recently used for NDT because it is more expensive and time consuming than conventional X-ray imaging. Nevertheless, there are applications where simple radiography provides only poor results because of superimposed object layers. This article discusses NDT specific problems of CT such as beam hardening and shows some microelectronic applications benefiting from CT as well as examples where modifications of the standard CT procedure are necessary to gain depth information about the object. This so called limited angle tomography reaches a higher image resolution than CT when flat modules are tested.