Promotional videos are rapidly becoming a popular medium for persuading people to change their behaviours in many settings (e.g., online shopping, social enterprise initiatives). Today, such videos are often produced by professionals, which is a time-, labour-and cost-intensive undertaking. In order to produce such contents to support a large applications (e.g., e-commerce), the field of artificial intelligence (AI)-empowered persuasive video generation (AIPVG) has gained traction in recent years. This field is interdisciplinary in nature, which makes it challenging for new researchers to grasp. Currently, there is no comprehensive survey of AIPVG available. In this paper, we bridge this gap by reviewing key AI techniques that can be utilized to automatically generate persuasive videos. We offer a first-of-its-kind taxonomy which divides AIPVG into three major steps: 1) visual material understanding, which extracts information from the visual materials (VMs) relevant to the target of promotion; 2) visual storyline generation, which shortlists and arranges high-quality VMs into a sequence in order to compose a storyline with persuasive power; and 3) post-production, which involves background music generation and still image animation to enhance viewing experience. We also introduce the evaluation metrics and datasets commonly adopted in the field of AIPVG. We analyze the advantages and disadvantages of the existing works belonging to the above-mentioned steps, and discuss interesting potential future research directions.