This paper reviews how neoclassical (NC) transport analyses have been exploited to predict/understand the improved confinement achieved in the Large Helical Device (LHD), such as high-temperature and/or high-density regimes. Recent high-performance LHD plasmas have provided a good opportunity to test/verify the impact of the radial electric field (Er) for reducing the NC transport in the low-collisionality regime. The bifurcative nature of Er to the electron root was clarified to be the background physics for the improved electron heat confinement in the core region. The ion root has been verified with measurement as predicted from the NC ambipolarity for the high-ion temperature plasmas. The construction of the NC diffusion coefficient database has been advanced for making accurate and fast NC calculations available. The predicted dependence of the bootstrap current on the magnetic configuration has also been experimentally verified. The extension of NC transport theory itself has been greatly motivated by the extension of the plasma parameters. Code development for the inclusion of the finite orbit width effect and the progress of the moment approach are explained as such examples.