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Graphs are commonly used for representing complex structures such as social relationships, biological interactions, and knowledge bases. In many scenarios, graphs not only represent topological relationships but also store the attributes that denote the semantics associated with their vertices and edges, known as attributed graphs. Attributed graphs can meet demands for a wide range of applications, and thus a variety of queries on attributed graphs have been proposed. However, these diverse types of attributed graph queries have not been systematically investigated yet. In this paper, we provide an extensive survey of several typical types of attributed graph queries. We propose a taxonomy of attributed graph queries based on query inputs and outputs. We summarize the definitions of queries that fall into each category and present a fine-grained classification of queries within each category by analyzing the semantics and algorithmic motivations behind these queries. Moreover, we discuss the insights of how existing studies address the technical challenges of query processing and outline several promising future research directions.