Lithium niobate (LN) exhibits unique material characteristics that have found many important applications. Scaling LN devices down to a nanoscopic scale can dramatically enhance light-matter interaction that would enable nonlinear and quantum photonic functionalities beyond the reach of conventional means.However, developing LN-based nanophotonic devices turns out to be nontrivial. Although significant efforts have been devoted in recent years, LN photonic crystal structures developed to date exhibit fairly low quality. Here we demonstrate LN photonic crystal nanobeam resonators with optical Q as high as 10 5 , more than two orders of magnitude higher than other LN nanocavities reported to date. The high optical quality together with tight mode confinement leads to extremely strong nonlinear photorefractive effect, with a resonance tuning rate of ∼0.64 GHz/aJ, or equivalently ∼84 MHz/photon, three orders of magnitude greater than other LN resonators. In particular, we observed intriguing quenching of photorefraction that has never been reported before. The devices also exhibit strong optomechanical coupling with gigahertz nanomechanical mode with a significant f · Q product of 1.47 × 10 12 Hz. The demonstration of high-Q LN photonic crystal nanoresonators paves a crucial step towards LN nanophotonics that could integrate the outstanding material properties with versatile nanoscale device engineering for diverse intriguing functionalities. * These authors contributed equally to this work. † Electronic address: qiang.lin@rochester.edu 1 arXiv:1706.08904v2 [physics.optics]