Few-shot learning on heterogeneous graphs (FLHG) is attracting more attention from both academia and industry because prevailing studies on heterogeneous graphs often suffer from label sparsity. FLHG aims to tackle the performance degradation in the face of limited annotated data and there have been numerous recent studies proposing various methods and applications. In this paper, we provide a comprehensive review of existing FLHG methods, covering challenges, research progress, and future prospects. Specifically, we first formalize FLHG and categorize its methods into three types: single-heterogeneity FLHG, dual-heterogeneity FLHG, and multi-heterogeneity FLHG. Then, we analyze the research progress within each category, highlighting the most recent and representative developments. Finally, we identify and discuss promising directions for future research in FLHG. To the best of our knowledge, this paper is the first systematic and comprehensive review of FLHG.