Single-crystalline silicon carbide is an attractive material for power electronics. However, it is difficult to achieve the direct bonding of SiC to conventional Si-based materials (e.g., Si, SiO2, and glass) due to the large mismatch in coefficients of thermal expansion and lattice constants. To solve the bottleneck, we present a facile direct bonding method using vacuum ultraviolet (VUV) surface irradiation for a robust combination of SiC to Si, SiO2, and glass at low temperatures (<= 200 degrees C). The mechanisms behind the VUV-irradiated bonding of SiC to Si-based materials were also investigated. According to surface characterizations, VUV irradiation can lead to smooth and hydrophilic surfaces, which are beneficial for direct bonding in humid air. The tight and defect-free SiC/Si, SiC/SiO2 and SiC/glass bonding interfaces were confirmed by transmission electron microscopy. In particular, the enriched carbon transition layers were formed on the side of silicon carbide because of the oxidation and sputtering of Si atoms during VUV irradiation. This will possibly improve the bonding interfaces and contribute to the enhanced bonding strengths. Moreover, the SiC/glass bonded pair exhibited relatively high optical transparency in the UV-Vis range. Therefore, the direct bonding of single-crystalline SiC and heterostructure Si-based materials offers great potentials for high-performance power electronics, as well as micro/nanofluidic devices.