Direct epitaxial growth of III-V heterostructure on CMOS-compatible silicon wafer offers substantial manufacturing cost and scalability advantages. Quantum dot (QD) devices are less sensitive to defect and temperature, which makes epitaxially grown III-V QD lasers on Si one of the most promising technologies for achieving low-cost, scalable integration with silicon photonics. The major challenges are that heteroepitaxial growth of III-V materials on Si normally encounters high densities of mismatch dislocations, antiphase boundaries and thermal cracks, which limit the device performance and lifetime. This paper reviews some of the recent developments on hybrid InAs/GaAs QD growth on Ge substrates and highly uniform (111)-faceted hollow Si (001) substrates by molecular beam epitaxy (MBE). By implementing step-graded epitaxial growth techniques, the emission wavelength can be tuned into either an O band or C/L band. Furthermore, microcavity QD laser devices are fabricated and characterized. The epitaxially grown III-V/IV hybrid platform paves the way to provide a promising approach for future on-chip silicon photonic integration.