Transport in networks represents a class of important phenomena that occur in many natural and anthropogenic settings. This dissertation deals with two such processes: heat transport in fracture networks in the subsurface and resiliency response of a cyber network to virus propagation. Numerical simulations of heat transfer provide insight into the performance of subsurface systems (e.g. geothermal reservoirs) and the potential for their enhancement. Standard, grid-based method of heat transfer are computationally expensive, often prohibitively so [Karra et al., 2018], due to a vast discrepancy of scales between fracture apertures (millimeter scale) and the ambient rock matrix domain (meter scale). In Chapter 2, we present a mesh-free time-domain particle method for modeling heat transfer in highly heterogeneous fractured media. Our method is orders of magnitude faster than its grid-based alternatives and is readily adaptable to different network configurations. We deploy this method to model heat extraction from geothermal reservoirs by using a fractal network representing faults and damage zones. Our analysis reveals anomalous behavior of heat transfer in fractured environments due to existence of preferential flow paths. It also demonstrates a significant impact of the networks topology on the performance of geothermal reservoirs. In Chapter 3, this method is used to investigate the impact of fracture network properties on geothermal performance. Specifically, we explore how fracture-network topology and matrix-block size distribution control, respectively, the advective and conductive mechanisms of heat transfer in fractures and ambient matrix, as well as the heat flux exchanged between these structures. To accomplish this goal, we examine two different conceptual descriptors of fracture networks over a variety of hydraulic conditions and fracture-generating parameters, and the effects of topologic properties and hydraulic conditions on computational time. In Chapter 4 we further generalize our mesh-free particle method by removing the physical assumption of one-dimensional conduction in the matrix. This is achieved by accounting for both longitudinal and transversal heat conduction in the matrix. It looks at the impact of removing set assumption and identifies the parameter set where it is of importance. Finally, in Chapter 5, we explore transport in anthropogenic networks by presenting a method to simulate the resiliency response of a cyber network to a virus propagation. We identify the need for systematic data collection and appropriate metrics to enable data driven optimization of the rule base. As well as demonstrate that the optimal number of rules necessary to regulate a cyber network efficiently is likely to be small and focused on specific critical functions that the system needs to maintain.