This review summarizes recent studies of thermal transport in nanoscaled semiconductors. Different from bulk materials, new physics and novel thermal properties arise in low dimensional nanostructures, such as the abnormal heat conduction, the size dependence of thermal conductivity, phonon boundary/edge scatterings. It is also demonstrated that phonons transport super-diffusively in low dimensional structures, in other words, Fourier's law is not applicable. Based on manipulating phonons, we also discuss envisioned applications of nanostructures in a broad area, ranging from thermoelectrics, heat dissipation to phononic devices.