Dynamic networks have recently being recognized as a powerful abstraction to model and represent the temporal changes and dynamic aspects of the data underlying many complex systems. This recognition has resulted in a burst of research activity related to modeling, analyzing, and understanding the properties, characteristics, and evolution of such dynamic networks. The focus of this growing research has been mainly defining important recurrent structural patterns and developing algorithms for their identification. Most of these tools are not designed to identify time-persistent relational patterns or do not focus on tracking the changes of these relational patterns over time. Analysis of temporal aspects of the entity relations in these networks can provide significant insight in determining the conserved relational patterns and the evolution of such patterns over time. Computational methods and tools that can efficiently and effectively analyze the changes in dynamic relational networks can substantially expand the types and diversity of dynamic networks that can be analyzed and the information that can be gained from such analysis. This may provide information on the recurrence and the stability of its relational patterns, help in the detection of abnormal patterns potentially indicating fraudulent or other malevolent behaviors, and improve the ability to predict the relations and their changes in these networks. In this dissertation we present new data mining methods for analyzing the temporal evolution of relations between entities of relational networks. Different classes of evolving relational patterns are introduced that are motivated by considering two distinct aspects of relational pattern evolution. The first is the notion of state transition and seeks to identify sets of entities whose time-persistent relations change over time and space. The second is the notion of coevolution and seeks to identify recurring sets of entities whose relations change in a consistent way over time and space. We first present a new class of patterns, referred as the evolving induced relational states (EIRS), which is designed to analyze the time-persistent relations or states between the entities of the dynamic networks. These patterns can help identify the transitions from one conserved state to the next and may provide evidence to the existence of external factors that are responsible for changing the stable relational patterns in these networks. We developed an algorithm to efficiently mine all maximal non-redundant evolution paths of the stable relational states of a dynamic network. Next we introduce a class of patterns, referred to as coevolving relational motifs (CRM), which is designed to identify recurring sets of entities whose relations change in a consistent way over time. CRMs can provide evidence to the existence of, possibly unknown, coordination mechanisms by identifying the relational motifs that evolve in a similar and highly conserved fashion. An algorithm is presented to efficiently analyze the frequent relational changes between the entities of the dynamic networks and capture all frequent coevolutions as CRMs. At last, we define a new class of patterns built upon the concepts of CRMs, referred as coevolving induced relational motifs (CIRM), is designed to represent patterns in which all the relations among recurring sets of nodes are captured and some of the relations undergo changes in a consistent way across different snapshots of the network. We also present an algorithm to efficiently mine all frequent coevolving induced relational motifs.A comprehensive evaluation of the performance and scalability of all the algorithms is presented through extensive experiments using multiple dynamic networks derived from real world datasets from various application domains. The detailed analysis of the results from the experiments illustrate the efficiency of these algorithms. In addition, we provide a qualitative analysis of the information captured by each class of the discovered patterns. For example, we show that some of the discovered CRMs capture relational changes between the nodes that are thematically different (i.e., edge labels transition between two clusters of topics that have very low similarity). Moreover, some of these patterns are able to capture network characteristics that can be used as features for modeling the underlying dynamic network.The new classes of evolving patterns and the algorithms can enable the effective analysis of complex relational networks towards the goal of better understanding of their temporal changes. Knowing these patterns provides strong observational evidence of the existence of mechanisms that control, coordinate, and trigger these evolutionary changes, which can be used to focus further studies and analysis.