This seminar will present some of the more methodological aspects linked to inversion techniques. After an introduction to the mathematical context, to concepts such as ill-posed problems, the variational principle of adiabatic stellar oscillations and regularization techniques, more focus will be given to the SOLA technique developed by Frank Pijpers and Michael J. Thompson in helioseismology. After having developed the aspects of the trade-off problem, the presentation will move on to the asteroseismic applications of this technique and will cover some problems associated to non-linearity, cross-terms contributions and the absence of knowledge on fundamental parameters such as the mass and radius of the observed target. In this context, obtaining new structural kernels is crucial and some examples of new kernels will be presented. Finally, we will conclude on perspectives for the study of convective cores and envelope using new indicators and asteroseismic inversions.