A covert communications network (CCN) is a connected, overlay peer-to-peer network used to support communications within a group in which the survival of the group depends on the confidentiality and anonymity of communications, on concealment of participation in the network to both other members of the group and external eavesdroppers, and finally on resilience against disconnection. In this dissertation, we describe the challenges and requirements for such a system. We consider the topologies of resilient covert communications networks that: (1) minimize the impact on the network in the event of a subverted node; and (2) maximize the connectivity of the survivor network with the removal of the subverted node and its closed neighborhood. We analyze the properties of resilient covert networks, propose measurements for determining the suitability of a topology for use in a covert communication network, and determine the properties of an optimal covert network topology. We analyze multiple topologies and identify two constructions that are capable of generating optimal topologies. We then extend these constructions to produce near-optimal topologies that can “grow” as new nodes join the network. We also address protocols for membership management and routing. Finally, we describe the architecture of a prototype system for instantiating a CCN.