We review the results of our research on damage mechanisms in materials irradiated with femtosecond free-electron-laser (FEL) pulses. They were obtained using our hybrid approach, X-ray-induced thermal and non-thermal transitions (XTANT). Various damage mechanisms are discussed with respect to the pulse fluence and material properties on examples of diamond, amorphous carbon, C 60 crystal, and silicon. We indicate the following conditions: those producing thermal melting of targets as a result of electron-ion energy exchange; non-thermal phase transitions due to modification of the interatomic potential; Coulomb explosion due to accumulated net charge in finite-size systems; spallation or ablation at higher fluences due to detachment of sample fragments; and warm dense matter formation. Transient optical coefficients are compared with experimental data whenever available, proving the validity of our modeling approach. Predicted diffraction patterns can be compared with the results of ongoing or future FEL experiments. Limitations of our model and possible future directions of development are outlined.