We have very recently re-determined the abundances of nearly all the available chemical elements in the solar photosphere, from lithium to thorium (Asplund et al. Annu. Rev. Astron. Astrophys. 47, 481 (2009)). This new complete and homogeneous analysis results from a very careful selection of spectral lines of all the indicators of the abundances present in the solar photospheric spectrum, from a discussion of the atomic and molecular data, and from an analysis of these lines based on a new 3D model of the solar outer layers, taking non-LTE effects into account when possible. We present these new results, compare them with other recent solar data as well as with recent results for the solar neighborhood, and discuss some of their most important implications as well as some of the atomic data we still urgently need.