Heterogeneous interactions between the components of a complex system give rise to diverse emergent functions. A key goal in the study of such systems is to derive an understanding of their structure-function relationship. Such an understanding has implications for crafting interventions in existing systems and for designing new systems with favorable properties. Network science has developed a broad range of tools to conceptualize complex systems as networks and to examine them in relation to observable system behaviors. A fundamental approach relies on characterizing the evolution of temporally coupled state-based network dynamics.This method assumes that the spread of dynamics is primarily responsible for a network's behavioral properties. Yet, the structure of many complex systems is also subject to constant change. Components may be added or removed, and the strength of their relationships may vary with time. Therefore, parallel efforts in network science have sought to characterize structural dynamics separately from temporal dynamics. In this dissertation, we examine both temporal and structural network dynamics in the context of underlying goals or motivations for complex systems.The goals may be temporal, relating to favorable dynamical states, or structural, relating to favorable network topologies. Chapter 2 is a case study from network neuroscience on goal-directed temporal dynamics. Specifically, we investigate the role of community structure in the controllability of brain networks. Chapter 3 examines walk dynamics on networks by conceptualizing human curiosity as the goal-directed exploration of networked knowledge spaces. We treat knowledge as a dynamic subgraph induced by acquired units of information and use this characterization to study theoretical accounts of the motivations underlying human curiosity. Chapter 4 generalizes goal-directed network walks as agent-environment interactions. We build on our work on human curiosity to adapt topological cavities and network compressibility as explicit reward signals to drive graph exploration. Through this dissertation, we offer a comprehensive set of tools to study goal-directed network dynamics while simultaneously deepening our understanding of several domains of applied network science.