Graph-structured data, ranging from social networks to financial transaction networks, from citation networks to gene regulatory networks, have been widely used for modeling a myriad of real-world systems. As a prevailing model architecture to model graph-structured data, graph neural networks (GNNs) have drawn much attention in both academic and industrial communities in the past decades. Despite their success in different graph learning tasks, existing methods usually rely on learning from “big” data, requiring a large amount of labeled data for model training. However, it is common that real-world graphs are associated with “small” labeled data as data annotation and labeling on graphs is always time and resource-consuming. Therefore, it is imperative to investigate graph machine learning (graph ML) with low-cost human supervision for low-resource settings where limited or even no labeled data is available. This paper investigates a new research field—data-efficient graph learning, which aims to push forward the performance boundary of graph ML models with different kinds of low-cost supervision signals. Specifically, we outline the fundamental research problems, review the current progress, and discuss the future prospects of data-efficient graph learning, aiming to illuminate the path for subsequent research in this field.