In this talk, we will consider the third-order differential operators with distribution coefficients (generalized functions). We will focus on the inverse spectral problem, which consists in the recovery of the differential expression coefficients from the spectral data. Necessary and sufficient conditions for solvability of this inverse problem have been obtained by developing the method of spectral mappings. This talk is based on the results of the following paper: Bondarenko N. P., Inverse spectral problem for the third-order differential equation, Results in Mathematics, 78 (2023), Article Number: 179, (43 pages).