Electro-optic modulators (EOMs) are pivotal in bridging electrical and optical domains, essential for diverse applications including optical communication, microwave signal processing, sensing, and quantum technologies. However, achieving the trifecta of high-density integration, cost-effectiveness, and superior performance remains challenging within established integrated photonics platforms. Enter thin-film lithium niobate (LN), a recent standout with its inherent electro-optic (EO) efficiency, proven industrial performance, durability, and rapid fabrication advancements. This platform inherits material advantages from traditional bulk LN devices while offering a reduced footprint, wider bandwidths, and lower power requirements. Despite its recent introduction, commercial thin-film LN wafers already rival or surpass established alternatives like silicon and indium phosphide, benefitting from decades of research. In this review, we delve into the foundational principles and technical innovations driving state-of-the-art LN modulator demonstrations, exploring various methodologies, their strengths, and challenges. Furthermore, we outline pathways for further enhancing LN modulators and anticipate exciting prospects for larger-scale LN EO circuits beyond singular components. By elucidating the current landscape and future directions, we highlight the transformative potential of thin-film LN technology in advancing electro-optic modulation and integrated photonics.