In graph machine learning, data collection, sharing, and analysis often involve multiple parties, each of which may require varying levels of data security and privacy. To this end, preserving privacy is of great importance in protecting sensitive information. In the era of big data, the relationships among data entities have become unprecedentedly complex, and more applications utilize advanced data structures (i.e., graphs) that can support network structures and relevant attribute information. To date, many graph-based AI models have been proposed (e.g., graph neural networks) for various domain tasks, like computer vision and natural language processing. In this paper, we focus on reviewing privacy-preserving techniques of graph machine learning. We systematically review related works from the data to the computational aspects. We first review methods for generating privacy-preserving graph data. Then we describe methods for transmitting privacy-preserved information (e.g., graph model parameters) to realize the optimization-based computation when data sharing among multiple parties is risky or impossible. In addition to discussing relevant theoretical methodology and software tools, we also discuss current challenges and highlight several possible future research opportunities for privacy-preserving graph machine learning. Finally, we envision a unified and comprehensive secure graph machine learning system.