The interest of molecular double core holes was predicted in 1986 by Cederbaum et al who showed that their spectroscopy can be more informative than that of the single core holes, especially when the holes are located at different sites in the molecule (Cederbaum et al J. Chem. Phys. 85 (1986) 6513). Their experimental study in single photon formation had to await 2009-2010 with progress in synchrotron sources and development of efficient multi-electron coincidence experiments based on a magnetic bottle time of flight spectrometer. At the same time the advent of X-rays Free Electron Lasers opened the possibilty to create them in a two-photon process, and motivated new theoretical studies of their properties. We will illustrate here with a few examples, the progress done recently in the field, including formation of double core holes by double core photoionization, their spectroscopy and decay paths, and the related process of simultaneous core ionization and core excitation.