The lithium niobate crystal is a multifunctional optical material with excellent comprehensive properties. For the past decades, lithium niobate crystal has attracted significant attention in optics researches. Recently, lithium niobate on insulator (LNOI), also known as lithium niobate thin film (LNTF), has been considered as a revolutionary technology in optics that rejuvenates lithium niobate for LNOI-based integrated photonics. A LNTF is irreplaceable in frequency conversion since it is one of the best nonlinear crystals. In this study, we summarize the most recent progress of LNTF in nonlinear frequency conversions, such as second-order nonlinearities, third-order nonlinearities, cascaded nonlinearities, and optical frequency comb. Finally, we present the prospect for photonic integrated circuits (PIC) on the LNOI platform.