  Helioseismology has provided very detailed information about the solar
interior, and extensive data on a large number of stars, although at less
detail, are promised by the ongoing and upcoming asteroseismic projects. In the
solar case there remain serious challenges in understanding the inferred solar
structure, particularly in the light of the revised determinations of the solar
surface composition. Also, a secure understanding of the origins of solar
rotation as inferred from helioseismology, both in the radiative interior and
in the convection zone, is still missing. In the stellar case challenges are
certain to appear as the data allow more detailed inferences of the properties
of stellar cores. Large remaining uncertainties in modelling concerns the
properties of convective cores and other processes that may cause mixing. As a
result of developing asteroseismic signatures addressing these and other
issues, we can look forward to a highly challenging, and hence exciting, era of
stellar astrophysics.
