Silicon has been a core material for digital computing owing to its high mobility, stability oxide interface, mature manufacturing technologies for more than half a century. While Moore’s law seems to further advance via various technologies to extend its expiration date, some intractable problems that requires processing times growing exponentially cannot be solved in a reasonable scale of time. Meanwhile, quantum computing is a promising tool to perform calculations much more efficiently than classical computing for certain types of problems. To realize a practical quantum computer, quantum dots on group-IV semiconductor heterostructures are promising due to the long decoherence time, scalability, and compatibility with the Si VLSI technology. In this review, we start with the advancement of group-IV undoped heterostructures since 2000 and review carrier transport properties in these undoped heterostructure. We also review the hole effective masses, spin-orbit coupling, and effective g-factors in the Ge-based heterostructures and conclude with a brief summary.