Such fits evidently lead to the determination of the parameters characterizing a given set of model calculations but do not in themselves provide a challenge to stellar structure. A challenge may show up, however, as an inconsistency between the resulting models and other, independent, observations of the star; this underlines the importance of including other types of stellar observations in the analysis of asteroseismic **data** (Molenda-Żakowicz et al. 2010). A formal expression of the level of challenge to the model calculations is obtained if, as is often the case, the model frequencies and other properties differ significantly from the corresponding observed values (assuming, of course, that a reliable measure of the uncertainties in the latter is available). In this case more sophisticated types of analysis are required to determine the origin of the differences, very likely leading to true challenges to the theory of stellar evolution. Such analyses may concentrate on specific features in the star, such as the borders of convective regions (see Section 6 below). Alternatively, it may be possible in a limited way to carry out inverse analyses to infer the differences between the model and stellar structure (e.g., Basu et al. 2002;Roxburgh 2004).