Transition metal borides are known due to their attractive mechanical, electronic, refractive, and other properties. A new class of rhenium borides was identified by synchrotron single-crystal X-ray diffraction experiments in laser-heated diamond anvil cells between 26 and 75 GPa. Recoverable to ambient conditions, compounds rhenium triboride (ReB₃) and rhenium tetraboride (ReB₄) consist of close-packed single layers of rhenium atoms alternating with boron networks built from puckered hexagonal layers, which link short bonded (∼1.7 Å) axially oriented B₂ dumbbells. The short and incompressible Re–B and B–B bonds oriented along the hexagonal c-axis contribute to low axial compressibility comparable with the linear compressibility of diamond. Sub-millimeter samples of ReB₃ and ReB₄ were synthesized in a large-volume press at pressures as low as 33 GPa and used for material characterization. Crystals of both compounds are metallic and hard (Vickers hardness, H_V = 34(3) GPa). Geometrical, crystal-chemical, and theoretical analysis considerations suggest that potential ReB_x compounds with x > 4 can be based on the same principle of structural organization as in ReB₃ and ReB₄ and possess similar mechanical and electronic properties.