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To ensure survival and reproduction, individual animals navigating the world must regularly sense their surroundings and use this information for important decision-making. The same is true for animals living in groups, where the roles of sensing, information propagation, and decision-making are distributed on the basis of individual knowledge, spatial position within the group, and more. This review highlights key examples of temporal and spatiotemporal dynamics in animal group decision-making, emphasizing strong connections between mathematical models and experimental observations. We start with models of temporal dynamics, such as reaching consensus and the time dynamics of excitation-inhibition networks. For spatiotemporal dynamics in sparse groups, we explore the propagation of information and synchronization of movement in animal groups with models of self-propelled particles, where interactions are typically parameterized by length and timescales. In dense groups, we examine crowding effects using a soft condensed matter approach, where interactions are parameterized by physical potentials and forces. While focusing on invertebrates, we also demonstrate the applicability of these results to a wide range of organisms, aiming to provide an overview of group behavior dynamics and identify new areas for exploration.