SnxSey crystalline compounds consisting of Sn and Se atoms of varying compositions are systematically investigated at pressures from 0 to 100 GPa using the first-principles evolutionary crystal structure search method based on density functional theory. All known experimental phases of SnSe and SnSe2 are found without any prior input. A second-order polymorphic phase transition from SnSe-Pnma phase to SnSe-Cmcm phase is predicted at 2.5 GPa. Initially being semiconducting, this phase becomes metallic at 7.3 GPa. Upon further increase of pressure up to 36.6 GPa, SnSe-Cmcm phase is transformed to CsCl-type SnSe-Pm3m phase, which remains stable at even higher pressures. A metallic compound with different stoichiometry, Sn3Se4-I43d, is found to be thermodynamically stable from 18 to 70 GPa. Known semiconductor tin diselenide SnSe2-P3m1 phase is found to be thermodynamically stable from ambient pressure up to 18 GPa. Initially being semiconducting, it experiences metallization at pressures above 8 GPa.