Many big data applications in business and science require the management and analysis of huge amounts of graph data. Suitable systems to manage and to analyze such graph data should meet a number of challenging requirements including support for an expressive graph data model with heterogeneous vertices and edges, powerful query and graph mining capabilities, ease of use as well as high performance and scalability. In this chapter, we survey current system approaches for management and analysis of "big graph data". We discuss graph database systems, distributed graph processing systems such as Google Pregel and its variations, and graph dataflow approaches based on Apache Spark and Flink. We further outline a recent research framework called Gradoop that is build on the so-called Extended Property Graph Data Model with dedicated support for analyzing not only single graphs but also collections of graphs. Finally, we discuss current and future research challenges.