This thesis investigated the recovery of critical metals from waste streams, by means of (bio)hydrometallurgical leaching and bio-precipitation. The literature reviews covered urban solid wastes and coal ashes containing rare earth elements (REEs). The numerical investigations focused on three critical metals: Arsenic (As) contained in metal-contaminated natural waters, and Europium (Eu) and Ytterbium (Yb) contained in silicate rocks that often are accumulated as lowvalue mine tailings. This thesis utilized geochemical modeling, using The Geochemist’s Workbench software, to develop and test reactive models. The first model simulates the timedependent bio-precipitation of arsenic from a natural water with the aid of bacterium Bacillus arsenicoselenatis. The second model simulates the equilibration of four silicate minerals (chrysotile, forsterite, montmorillonite and phlogopite) containing oxides of Eu and Yb with an aqueous solution of dilute salts exposed to air, followed by the addition of inorganic (H2SO4 and HCl) and organic (Lactic) acids to this system.