In the first part of the talk, we will describe the results on soft diffraction and give some details about the odderon discovery by the TOTEM and D0 experiments. In a second part of the talk, we will describe the study of inclusive and exclusive diffraction at low and high masses following the experience at HERA. Results on diffraction at the LHC will pave the road of future results to be obtained at the EIC and we will describe the present results and perspectives at the LHC. We will also mention briefly the search for quartic anomalous couplings and axion-like particles using tagged protons in the final state and heavy ion interactions.