Open issues in probing interiors of solar-like oscillating main sequence stars 1. From the Sun to nearly suns

We review some major, open issues in the current modelling of low and intermediate mass, main sequence stars based on seismological studies. In the present paper, the solar case is discussed together with current problems that are common to the Sun and stars with a structure similar to that of the Sun. Several additional issues specific to main sequence stars other than the Sun are reviewed and illustrated with a few stars observed with CoRoT in a companion paper.