The international activities in developing new flaw characterization methods with special emphasis on acoustic imaging have been increased. To reduce the dependency upon amplitude information and due to the fact that flaw information is buried in the shape and fine structure of wave fronts, considerable attention has been given to the development of methods using time-of-flight information from different probe positions. For this reason, with mechanical scanners and specially build data acquisition and evaluation systems, a vareity of ways to produce images has been developed. These include echotomography, linear or two dimensional mono- or multi-frequency holography, tip echo interference methods, ALOK (amplitude-,time-of-flight-locus curves), Phased Array, SAFT or Rayleigh-Sommerfeld Holography. These methods use mathematical algorithms which seem to be independent or which have been derived heuristically. Based upon the concept of elastodynamic diffraction theory together with that of tomography a concept can be derived which reveals the inner connection of these algorithms. Differences in the reconstructions arise due to limitations like limited aperture, limited bandwidth, use of mode converted signals or due to complex surface shapes. An attempt is made to cover the theoretical background, to give an overview on existing data acquisition systems and to describe the strength, weaknesses, and difficulties in producing acoustic images.