In-band full-duplex is emerging as a promising solution to enhance throughput in wireless networks. Allowing nodes to simultaneously send and receive data over the same bandwidth can potentially double the system capacity, and a good degree of maturity has been reached for physical layer design, with practical demonstrations in simple topologies. However, the true potential of full-duplex at a system level is yet to be fully understood. In this paper, we introduce an analytical framework based on stochastic geometry that captures the behaviour of large full-duplex networks implementing an asynchronous random access policy based on Aloha. Via exact expressions we discuss the key tradeoffs that characterise these systems, exploring among the rest the role of transmission duration, imperfect self-interference cancellation and fraction of full-duplex nodes in the network. We also provide protocol design principles, and our comparison with slotted systems sheds light on the performance loss induced by the lack of synchronism.