Graph-structured data, prevalent in domains ranging from social networks to biochemical analysis, serve as the foundation for diverse real-world systems. While graph neural networks demonstrate proficiency in modeling this type of data, their success is often reliant on significant amounts of labeled data, posing a challenge in practical scenarios with limited annotation resources. To tackle this problem, tremendous efforts have been devoted to enhancing graph machine learning performance under low-resource settings by exploring various approaches to minimal supervision. In this paper, we introduce a novel concept of Data-Efficient Graph Learning (DEGL) as a research frontier, and present the first survey that summarizes the current progress of DEGL. We initiate by highlighting the challenges inherent in training models with large labeled data, paving the way for our exploration into DEGL. Next, we systematically review recent advances on this topic from several key aspects, including self-supervised graph learning, semi-supervised graph learning, and few-shot graph learning. Also, we state promising directions for future research, contributing to the evolution of graph machine learning.