The capacity scaling laws of two overlaid networks sharing the same wireless resources with different priorities are investigated. The primary network is assumed to operate in an order-optimal fashion to achieve its standalone capacity scaling law. The secondary “cognitive” network must keep its interference to the primary network below a certain threshold while at the same time maximizing its own throughput scaling law based on cognition information. The existing scaling results for cognitive networks inherently assume multihop communication treating all other signals except from a single intended transmitter as noise. By contrast, in this paper, a general coding model is considered without any specific physical layer coding assumptions. Therefore, this paper provides a general framework for comprehensive understanding of fundamental limits on the capacity scaling laws of cognitive networks. For the extended network model, the capacity scaling laws of both the primary and secondary networks are completely characterized. For the dense network model, an improved throughput scaling law is achieved by inducing cooperation within the secondary network. In both cases, it turns out that the conventional multihop approach is in general quite suboptimal.