Graphs are commonly employed to model complex data and discover latent patterns and relationships between entities in the real world. Canonical graph learning models have achieved remarkable progress in modeling and inference on graph-structured data that consists of nodes connected by edges. Generally, they leverage abundant labeled data for model training and thus inevitably suffer from the label scarcity issue due to the expense and hardship of data annotation in practice. Data-efficient graph learning attempts to address the prevailing data scarcity issue in graph mining problems, of which the key idea is to transfer knowledge from the related resources to obtain the models with good generalizability to the target graph-related tasks with mere annotations. However, the generalization of the models to data-scarce scenarios is faced with challenges including 1) dealing with graph structure and structural heterogeneity to extract transferable knowledge; 2) selecting beneficial and fine-grained knowledge for effective transfer; 3) addressing the divergence across different resources to promote knowledge transfer. Motivated by the aforementioned challenges, the dissertation mainly focuses on three perspectives, i.e., knowledge extraction with graph heterogeneity, knowledge selection, and knowledge transfer. The purposed models are applied to various node classification and graph classification tasks in the low-data regimes, evaluated on a variety of datasets, and have shown their effectiveness compared with the state-of-the-art baselines.