Network selection in Earth surface systems (ESS) operates at two general levels. First, the emergence of interconnected networks of flows and interactions often supports the efficiency and survival of the systems. Second, in many cases specific network topologies are advantageous in terms of efficiency and are selected for. The first part of the chapter addresses the question of how strongly connected networks form in ESS, and their selective advantages are demonstrated using graph theory. An example of a highly connected fluvial-wetland complex and its ability to absorb impacts of extreme river floods and storm surges is presented. Percolation theory, derived from graph theory and statistical mechanics, is briefly summarized. The theory accurately predicts the emergence of optimal flux networks in soil and groundwater flow, the hydrological cycle, and other phenomena, illustrating the tendency for high-efficiency networks to be selected. Remarkable regularity in the branching dendritic topology of fluvial channel networks has long been noted and investigated. Channel networks differ in detail, but the statistical properties and the general visual impression are remarkably consistent across a range of spatial scales and environments. This is due to network selection linked to flux efficiency and energy dissipation. Network selection is also evident in rock fracture networks. Scale-free networks may also be subject to positive selection in ESS, but evidence is still limited.