Abstract: The paper presents a short review of the modal representation and inversion techniques applied to problems of ocean acoustic tomography and geoacoustic inversion. The use of the modal inversion techniques is based on the assumption that the modal component of the acoustic field can be recognized in the recorded acoustic signals. The paper is referred to the main techniques that have been applied so far by the group of the Institute of Applied and Computational Mathematics at FORTH and address their benefits and drawbacks.