Male infertility contributes substantially to the global infertility burden, and sperm analysis remains central to diagnosis, treatment planning, and assisted reproductive technology. Conventional semen evaluation, however, is labor-intensive, operator-dependent, and limited by inter- and intra-observer variability, motivating the development of objective and reproducible computational approaches. This review provides a comprehensive and perspective-oriented synthesis of artificial intelligence-driven sperm analysis, with a focus on computer vision, deep learning, multimodal fusion, robustness, and clinical translation. We first review task-specific methods for sperm detection and counting, tracking-based motility assessment, semantic and instance segmentation, morphology and defect classification, functional assessment, and genetic integrity evaluation. We then summarize public datasets, benchmarks, evaluation metrics, and emerging multimodal strategies that integrate microscopic images, time-lapse videos, CASA-derived parameters, DNA integrity assays, and clinical metadata. Beyond algorithmic performance, we discuss key barriers to real-world deployment, including data scarcity, cross-center domain shift, annotation inconsistency, interpretability, uncertainty calibration, privacy-preserving learning, and workflow integration. Finally, we outline a staged clinical translation roadmap spanning technical standardization, multicenter retrospective validation, silent prospective evaluation, human-in-the-loop clinical testing, ART outcome validation, regulatory approval, and post-market monitoring. By organizing the field from task-specific visual recognition to trustworthy multimodal reproductive intelligence, this review highlights both the progress and the unresolved challenges required to translate AI-driven sperm analysis into clinically meaningful decision support.