Figural analogy problems have long been a widely used format in human intelligence tests. In the past four decades, more and more research has investigated automatic item generation for figural analogy problems, i.e., algorithmic approaches for systematically and automatically creating such problems. In cognitive science and psychometrics, this research can deepen our understandings of human analogical ability and psychometric properties of figural analogies. With the recent development of data-driven AI models for reasoning about figural analogies, the territory of automatic item generation of figural analogies has further expanded. This expansion brings new challenges as well as opportunities, which demand reflection on previous item generation research and planning future studies. This paper reviews the important works of automatic item generation of figural analogies for both human intelligence tests and data-driven AI models. From an interdisciplinary perspective, the principles and technical details of these works are analyzed and compared, and desiderata for future research are suggested.