Efficient processing of large-scale graphs in distributed environments has been an increasingly popular topic of research in recent years. Inter-connected data that can be modeled as graphs arise in application domains such as machine learning, recommendation, web search, and social network analysis. Writing distributed graph applications is inherently hard and requires programming models that can cover a diverse set of problem domains, including iterative refinement algorithms, graph transformations, graph aggregations, pattern matching, ego-network analysis, and graph traversals. Several high-level programming abstractions have been proposed and adopted by distributed graph processing systems and big data platforms. Even though significant work has been done to experimentally compare distributed graph processing frameworks, no qualitative study and comparison of graph programming abstractions has been conducted yet. In this survey, we review and analyze the most prevalent high-level programming models for distributed graph processing, in terms of their semantics and applicability. We identify the classes of graph applications that can be naturally expressed by each abstraction and we also give examples of applications that are hard or impossible to express. We review 34 distributed graph processing systems with respect to their programming abstractions, execution models, and communication mechanisms. Finally, we discuss trends and open research questions in the area of distributed graph processing.