Generative AI (GenAI) has witnessed remarkable progress in recent years and demonstrated impressive performance in various generation tasks in different domains such as computer vision and computational design. Many researchers have attempted to integrate GenAI into visualization framework, leveraging the superior generative capacity for different operations. Concurrently, recent major breakthroughs in GenAI like diffusion model and large language model have also drastically increase the potential of GenAI4VIS. From a technical perspective, this paper looks back on previous visualization studies leveraging GenAI and discusses the challenges and opportunities for future research. Specifically, we cover the applications of different types of GenAI methods including sequence, tabular, spatial and graph generation techniques for different tasks of visualization which we summarize into four major stages: data enhancement, visual mapping generation, stylization and interaction. For each specific visualization sub-task, we illustrate the typical data and concrete GenAI algorithms, aiming to provide in-depth understanding of the state-of-the-art GenAI4VIS techniques and their limitations. Furthermore, based on the survey, we discuss three major aspects of challenges and research opportunities including evaluation, dataset, and the gap between end-to-end GenAI and generative algorithms. By summarizing different generation algorithms, their current applications and limitations, this paper endeavors to provide useful insights for future GenAI4VIS research.