Advances in surgical video analysis are transforming operating rooms into intelligent, data-driven environments. Computer-assisted systems support full surgical workflow, from preoperative planning to intraoperative guidance and postoperative assessment. However, developing robust and generalizable models for surgical video understanding remains challenging due to (I) annotation scarcity, (II) spatiotemporal complexity, and (III) domain gap across procedures and institutions. This doctoral research aims to bridge the gap between deep learning-based surgical video analysis in research and its real-world clinical deployment. To address the core challenge of recognizing surgical phases, actions, and events, critical for analysis, I benchmarked state-of-the-art neural network architectures to identify the most effective designs for each task. I further improved performance by proposing novel architectures and integrating advanced modules. Given the high cost of expert annotations and the domain gap across surgical video sources, I focused on reducing reliance on labeled data. We developed semi-supervised frameworks that improve model performance across tasks by leveraging large amounts of unlabeled surgical video. We introduced novel semi-supervised frameworks, including DIST, SemiVT-Surge, and ENCORE, that achieved state-of-the-art results on challenging surgical datasets by leveraging minimal labeled data and enhancing model training through dynamic pseudo-labeling. To support reproducibility and advance the field, we released two multi-task datasets: GynSurg, the largest gynecologic laparoscopy dataset, and Cataract-1K, the largest cataract surgery video dataset. Together, this work contributes to robust, data-efficient, and clinically scalable solutions for surgical video analysis, laying the foundation for generalizable AI systems that can meaningfully impact surgical care and training.