This chapter is devoted to anomaly detection in dynamic, attributed graphs. There has been a great deal of research on anomaly detection in graphs over the last decade, with a variety of methods proposed. This chapter discusses recent methods for anomaly detection in graphs,with a specific focus on detection within backgrounds based on random graph models. This sort of analysis can be applied for a variety of background models, which can incorporate topological dynamics and attributes of vertices and edges. The authors have developed a framework for anomalous subgraph detection in random background models, based on linear algebraic features of a graph. This includes an implementation in R that exploits structure in the random graph model for computationally tractable analysis of residuals. This chapter outlines this framework within the context of analyzing dynamic, attributed graphs. The remainder of this chapter is organized as follows. Section 2.2 defines the notation used within the chapter. Section 2.3 briefly describes a variety of perspectives and techniques for anomaly detection in graph-based data. Section 2.4 provides an overview of models for graph behavior that can be used as backgrounds for anomaly detection. Section 2.5 describes our framework for anomalous subgraph detection via spectral analysis of residuals, after the data are integrated over time. Section 2.6 discusses how the method described in Section 2.5 can be efficiently implemented in R using open source packages. Section 2.7 demonstrates the power of this technique in controlled simulation, considering the effects of both dynamics and attributes on detection performance. Section 2.8 gives a data analysis example within this context, using an evolving citation graph based on a commercially available document database of public scientific literature. Section 2.9 summarizes the chapter and discusses ongoing research in this area.