The burgeoning growth of video-to-music generation can be attributed to the ascendancy of multimodal generative models. However, there is a lack of literature that comprehensively combs through the work in this field. To fill this gap, this paper presents a comprehensive review of video-to-music generation using deep generative AI techniques, focusing on three key components: visual feature extraction, music generation frameworks, and conditioning mechanisms. We categorize existing approaches based on their designs for each component, clarifying the roles of different strategies. Preceding this, we provide a fine-grained classification of video and music modalities, illustrating how different categories influence the design of components within the generation pipelines. Furthermore, we summarize available multimodal datasets and evaluation metrics while highlighting ongoing challenges in the field.