Gossip algorithms are widely used in distributed signal processing for wireless sensor networks due to their robustness, lack of specialized routing, and energy efficiency. These algorithms allow nodes to exchange information and compute results without centralized control, making them suitable for large-scale, dynamic environments. This article reviews recent advances in gossip algorithms, focusing on their convergence rates, performance under wireless conditions, and applications in signal processing tasks such as distributed estimation, source localization, and compression. Gossip algorithms operate by iteratively exchanging information between nodes, with each node maintaining an estimate of the network average. In pairwise gossiping, two nodes exchange their estimates, and each updates their estimate to the average of the two. This process converges to the global average, provided the network is connected and nodes gossip frequently enough. However, pairwise gossip is slow on wireless networks, prompting research into faster algorithms. Faster gossip algorithms include geographic gossip, which uses node locations to direct information flow, and LADA, which uses partial location information and Markov chain lifting to accelerate convergence. These algorithms reduce the number of messages required and improve efficiency. Additionally, memory-based schemes and nested lattice quantizers have been proposed to enhance convergence rates and reduce error. Quantization is a key challenge in gossip algorithms, as it affects the accuracy of information exchange. Quantized consensus algorithms use discrete codes to approximate continuous values, but they can introduce errors and require careful design to ensure convergence. Theoretical analysis shows that the convergence rate depends on the network topology and the quantization strategy. Wireless channel coding is also important for gossip algorithms, as it ensures reliable communication over noisy channels. Techniques such as lattice codes and error-correcting codes help maintain the integrity of information exchanged between nodes. In sensor networks, gossip algorithms are applied to various tasks, including distributed estimation, source localization, and compression. These algorithms enable efficient computation within the network, reducing the need for data transmission to a central node and improving energy efficiency. Overall, gossip algorithms offer a flexible and robust approach to distributed signal processing in wireless sensor networks, with ongoing research aimed at improving their performance, efficiency, and adaptability to different network conditions.Gossip algorithms are widely used in distributed signal processing for wireless sensor networks due to their robustness, lack of specialized routing, and energy efficiency. These algorithms allow nodes to exchange information and compute results without centralized control, making them suitable for large-scale, dynamic environments. This article reviews recent advances in gossip algorithms, focusing on their convergence rates, performance under wireless conditions, and applications in signal processing tasks such as distributed estimation, source localization, and compression. Gossip algorithms operate by iteratively exchanging information between nodes, with each node maintaining an estimate of the network average. In pairwise gossiping, two nodes exchange their estimates, and each updates their estimate to the average of the two. This process converges to the global average, provided the network is connected and nodes gossip frequently enough. However, pairwise gossip is slow on wireless networks, prompting research into faster algorithms. Faster gossip algorithms include geographic gossip, which uses node locations to direct information flow, and LADA, which uses partial location information and Markov chain lifting to accelerate convergence. These algorithms reduce the number of messages required and improve efficiency. Additionally, memory-based schemes and nested lattice quantizers have been proposed to enhance convergence rates and reduce error. Quantization is a key challenge in gossip algorithms, as it affects the accuracy of information exchange. Quantized consensus algorithms use discrete codes to approximate continuous values, but they can introduce errors and require careful design to ensure convergence. Theoretical analysis shows that the convergence rate depends on the network topology and the quantization strategy. Wireless channel coding is also important for gossip algorithms, as it ensures reliable communication over noisy channels. Techniques such as lattice codes and error-correcting codes help maintain the integrity of information exchanged between nodes. In sensor networks, gossip algorithms are applied to various tasks, including distributed estimation, source localization, and compression. These algorithms enable efficient computation within the network, reducing the need for data transmission to a central node and improving energy efficiency. Overall, gossip algorithms offer a flexible and robust approach to distributed signal processing in wireless sensor networks, with ongoing research aimed at improving their performance, efficiency, and adaptability to different network conditions.