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The capacity scaling law of wireless networks has been considered as one of the most fundamental issues. In this survey, we aim at providing a comprehensive overview of the development in the area of scaling laws for throughput capacity and delay in wireless networks. We begin with background information on the notion of throughput capacity of random networks. Based on the benchmark random network model, we then elaborate the advanced strategies adopted to improve the throughput capacity, and other factors that affect the scaling laws. We also present the fundamental tradeoffs between throughput capacity and delay under a variety of mobility models. In addition, the capacity and delay for hybrid wireless networks are surveyed, in which there are at least two types of nodes functioning differently, e.g., normal nodes and infrastructure nodes. Finally, recent studies on scaling law for throughput capacity and delay in emerging vehicular networks are introduced.