Our recent experimental results of Ge nanoheteroepitaxy (NHE) on Si nanopillars (NPs) are reviewed to confirm the possibility of relaxed Ge growth on Si without misfit dislocations (MDs) formation by elastic deformation. Selective Ge growth is performed by using reduced pressure chemical vapor deposition (CVD) on two types of Si NPs with thermal SiO2 or CVD SiO2 sidewalls and on Si nanoislands (NIs) on SiO2. By using thermal SiO2 sidewall, compressive strain is generated in the Si pillar and fixed by the thermal SiO2. This results in an incoherent Ge growth on Si NPs due to MD formation. By using CVD SiO2 sidewall, tensile strain formation due to thermal expansion during prebake for Ge epi process is observed. However, strain in Si due to Ge growth is not dominant. By introducing a Si0.5Ge0.5 buffer layer, no MD and stacking faults are observed by cross section TEM. The shape of Ge on Si NPs becomes more uniform due to improved crystal quality. On Si Nis on SiO2, a clear compliance effect is observed after Ge growth. Coherent growth of Ge on Si is also realized on Si NIs by using Si0.5Ge0.5 buffer.