Lithium niobate (LN) thin film has received much attention as an integrated photonic platform, due to its rich and great photoelectric characteristics, based on which various functional photonic devices, such as electro-optic modulators and nonlinear wavelength converters, have been demonstrated with impressive performance. As an important part of the integrated photonic system, the long-awaited laser and amplifier on the LN thin-film platform have made a series of breakthroughs and important progress recently. In this review paper, the research progress of lasers and amplifiers realized on lithium niobate thin film platforms is reviewed comprehensively. Specifically, the research progress on optically pumped lasers and amplifiers based on rare-earth ions doping of LN thin films is introduced. Some important parameters and existing limitations of the current development are discussed. In addition, the implementation scheme and research progress of electrically pumped lasers and amplifiers on LN thin-film platforms are summarized. The advantages and disadvantages of optically and electrically pumped LN thin film light sources are analyzed. Finally, the applications of LN thin film lasers and amplifiers and other on-chip functional devices are envisaged.