The existing experimental data for the γ decay of the stable N=Z doubly-odd nuclei and the β decay of the corresponding isospin multiplets is reviewed. The structure of the lightest nuclei with masses A≤14 is used to test and constrain ab initio nuclear theories. Most of the data were obtained in the second half of the last century and, in some cases, lack the needed precision for comparison with theoretical calculations. Recent spectroscopic studies in the lightest doubly-odd N = Z nuclei are discussed, as well as open problems related to the understanding of their structures and ideas for future experiments.