The asymmetry between matter and antimatter of the Universe is related to the violation of the CP symmetry, where C and P are the charge-conjugation and parity operators. The amount of CP violation predicted by the Standard Model (SM) of particle physics is not sufficient to explain our matter-dominated Universe and other sources of CP violation are expected to exist. The phenomenon of CP violation has been observed in the K- and B-meson systems, but not yet in the decay of any baryonic particle. It is important to measure the size and nature of these CP asymmetries in as many decay modes as possible, to determine whether they are consistent with the theory predictions or, if not, what extensions to the SM would be required to explain them. The LHCb experiment operating at the Large Hadron Collider (LHC) at CERN is collecting unprecedented statistics of beauty baryons allowing for the first time to study CP violation in these decays. We find evidence for CP violation in Lambdab -> p pi- pi+ pi- decays with a statistical significance corresponding to 3.3 standard deviations, including systematic uncertainties, which might bring to the discovery of CP violation in the baryon sector with additional statistics. An overview of recent LHCb searches for CP violation in baryon decays will be presented, and also prospects for the future. In addition, we discuss our recent proposal to search for electric dipole moment (EDM) of heavy baryons, which is sensitive to new sources of CP violation beyond the SM. This research program is based on a novel fixed-target experiment to be installed in the LHC and exploits the phenomenon of spin precession of channeled particles in bent crystals.