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This paper studies the problem of neighbor discovery in wireless networks, namely, each node wishes to discover and identify the network interface addresses (NIAs) of those nodes within a single hop. A novel paradigm, called compressed neighbor discovery is proposed, which enables all nodes to simultaneously discover their respective neighborhoods with a single frame of transmission, which is typically of a few thousand symbol epochs. The key technique is to assign each node a unique on-off signature and let all nodes simultaneously transmit their signatures. Despite that the radios are half-duplex, each node observes a superposition of its neighbors ’ signatures (partially) through its own off-slots. To identify its neighbors out of a large network address space, each node solves a compressed sensing (or sparse recovery) problem. Two practical schemes are studied. The first employs random on-off signatures, and each node discovers its neighbors using a noncoherent detection algorithm based on group testing. The second scheme uses on-off signatures based on a deterministic second-order Reed-Muller code, and applies a chirp decoding algorithm. The second scheme needs much lower signal-to-noise ratio (SNR) to achieve the same error performance. The complexity of the chirp decoding algorithm is sub-linear, so that it is in principle scalable to networks with billions of nodes with 48-bit IEEE 802.11 MAC addresses. The compressed neighbor discovery schemes are much more efficient than conventional random-access discovery, where nodes have to retransmit over many frames with random delays to be successfully discovered