Over the past decade, there has been a concerted effort to develop a  network science for studying physical, biological, social, and  information networks within a common framework.  In this talk, we  discuss a number of recent results in network science concerning   connectivity, information and epidemic spread, and robustness in large-scale networks with spatial location and mobility.  We first study connectivity and information/epidemic spread in  large-scale networks modelled by random geometric graphs with dynamic  on-off links.   Using a percolation-based perspective, we characterize  the scaling behavior of the delay for spreading broadcast information or  a virus in these networks.  We show that the dissemination delay  exhibits two behavioral regimes, corresponding to a phase transition of  the underlying network connectivity. When the dynamic network is in the  subcritical phase, ignoring propagation delays, the dissemination delay  scales linearly with the Euclidean distance between the sender and the  receiver. When the dynamic network is in the supercritical phase, the  delay scales sublinearly with the distance.  More interestingly, by  using a new analysis which maps a network of mobile nodes to a network of stationary nodes with dynamic links, we show that the above results  can be used to characterize information/epidemic spread in mobile networks.  Next, we study the resilience of networks to node failures.  In many  networks, the failure of a node depends on its degree, which may reflect  the amount of traffic load on the node, or the relative importance of  the node.  Furthermore, in networks carrying load, the failure of one  node can result in redistribution of the load onto other nearby nodes.  If these nodes fail due to excessive load, then this process can result  in a cascading failure.  From the percolation  perspective, the  resilience of the network can be characterized in terms of whether  correlated node failures lead to a large connected component of failed  nodes or not.  Using this approach, we obtain analytic conditions on the  existence or non-existence of correlated and cascading failures.  The above results have important implications for problems such as  cascading failures in power grids, the spread  of epidemics among humans,  and the dissemination of broadcast information in wireless communication networks.