The solar abundance of chemical elements play an important role in addressing such important issues as the formation, structure, and evolution of the Sun and the solar system, the origin of the chemical elements, the evolution of stars and galaxies. Despite the large number of papers published on this issue, debates about the solar composition of the Sun continue. In this talk we start summarizing the current understanding of the solar abundances of iron and CNO elements, which play a crucial role on the determination of the solar metallicity. We then pay especial attention to the impact of the quiet Sun magnetism on the determination of the abundances of these elements. The solar photosphere is significantly magnetized, due to the ubiquitous presence of a small-scale magnetic field whose mean strength is thought to be of the order of 100 gauss. Here we address the problem of the determination of the abundances of chemical elements taking into account the significant magnetization of the quiet Sun photosphere. To this end, we use 3D models of the quiet solar photosphere resulting from a state-of-the-art magneto-convection simulation with small-scale dynamo action where the net magnetic flux is zero. We conclude that if the magnetism of the quiet solar photosphere is mainly produced by a small-scale dynamo,then its impact on the determination of the solar abundance of iron and CNO elements is negligible.