Several diagnostic systems in magnetically confined fusion plasmas provide line-integrated measurements along chords, including bolometry, visible light, soft-Xray ~SXR!, or neutron diagnostics. The task of retrieval of spatial distribution of the plasma emissivity from the line-integrated measurements constitutes an important part of fusion data analyses. Solutions in general rely on the basic symmetries of the confining magnetic field. One-dimensional distribution ~profile! inversion is adequate in the case of constant emissivity on magnetic flux surfaces; however, a two-dimensional ~2-D! inversion is required whenever the poloidal symmetry breaks down, e.g., due to collective magnetohydrodynamic ~MHD! phenomena, impurities, or fast trapped particle effects. The emissivity distribution can be either retrieved iteratively via forward-fitting of the line integrals from the presumed local plasma emissivity or calculated directly from the measured line integrals using inversion techniques ~plasma tomography; see Ref. 1!. Clearly, the latter strategy has a considerable advantage of independence on plasma models but calls for a dense coverage of the plasma cross section by good measurements. The methods and challenges of inversion techniques in tomography of fusion plasmas are detailed in Sec. II.