  Asteroseismology has emerged as the best way to characterize the global and
internal properties of nearby stars. Often, this characterization is achieved
by fitting stellar evolution models to asteroseismic observations. The star
under investigation is then assumed to have the properties of the best-fitting
model, such as its age. However, the models do not fit the observations
perfectly. This is due to incorrect or missing physics in stellar evolution
calculations, resulting in predicted stellar structures that are discrepant
with reality. Through an inverse analysis of the asteroseismic data, it is
possible to go further than fitting stellar models, and instead infer details
about the actual internal structure of the star at some locations in its
interior. Comparing theoretical and observed stellar structures then enables
the determination of the locations where the stellar models have discrepant
structure, and illuminates a path for improvements to our understanding of
stellar evolution. In this invited review, we describe the methods of
asteroseismic inversions, and outline the progress that is being made towards
measuring the interiors of stars.
