Lithium niobate (LiNbO₃, LN) thin films have been extensively studied for applications in acoustic and photonic devices, due to their outstanding piezoelectric, ferroelectric and electro-optical properties. With the increasing demand for high speed and low latency wireless communication, LN thin films with high electromechanical coupling coefficients are very attractive to improve the performance of acoustic resonators for radio frequency filters. The current bottleneck for LN-based devices is the synthesis of high-quality LN thin films, which is typically fabricated by expensive and inefficient process of ion slicing and layer transfer from bulk single crystals. This review paper focuses on the direct growth of high-quality LN thin films, which has the potential to scale up and lower the cost of LN thin films. We first introduce the crystal structure and piezoelectric properties of LN, followed by an overview of the state-of-the-art LN acoustic resonators. After a summary of the challenges in the fabrication of LN thin films, we review the direct growth of LN thin films by sputtering, pulsed laser deposition, metalorganic chemical vapor deposition and molecular beam epitaxy. With the progress in optimizing the crystallinity and surface roughness, the quality of the LN thin films synthesized by direct growth has been greatly improved. As a result of the fast-growing industrial interests, we believe that the research works in direct growth of LN thin films will increase exponentially to achieve the same quality of the LN thin films as the bulk single crystals.