This article reviews recent advances in the study of evolutionary dynamics of group interactions on structured populations, including lattices, complex networks, and coevolutionary models. The focus is on the public goods game, which is a representative model for group interactions. The review highlights the importance of statistical physics, network science, and evolutionary game theory in understanding the dynamics of group interactions. Key findings include: 1. **Lattices**: Group interactions on lattices can lead to different outcomes compared to pairwise interactions. For example, the deterministic limit ($K \to 0$) is optimal for cooperation on triangular and kagomé lattices, while overlapping triangles in square and honeycomb lattices can enhance cooperation. 2. **Heterogeneities in Dynamics**: Heterogeneous payoff distributions and contributions can promote cooperation. Nonlinear benefit functions and strategic complexity, such as conditional cooperation and the presence of loners, also influence the evolution of cooperation. 3. **Complex Networks**: Social heterogeneity, characterized by degree distribution and clustering, significantly affects the evolution of cooperation. Heterogeneous networks enable complete cooperator dominance at lower values of the synergy factor compared to regular networks. Degree correlations and the presence of hubs play crucial roles in promoting cooperation. 4. **Bipartite Graphs**: To better capture the structure of real-world networks, bipartite graphs are used to account for both pairwise ties and group structures. This approach helps in understanding the impact of group size and composition on cooperation. The review concludes by discussing the challenges and open questions in the field, emphasizing the need for further research to fully understand the dynamics of group interactions in complex systems.This article reviews recent advances in the study of evolutionary dynamics of group interactions on structured populations, including lattices, complex networks, and coevolutionary models. The focus is on the public goods game, which is a representative model for group interactions. The review highlights the importance of statistical physics, network science, and evolutionary game theory in understanding the dynamics of group interactions. Key findings include: 1. **Lattices**: Group interactions on lattices can lead to different outcomes compared to pairwise interactions. For example, the deterministic limit ($K \to 0$) is optimal for cooperation on triangular and kagomé lattices, while overlapping triangles in square and honeycomb lattices can enhance cooperation. 2. **Heterogeneities in Dynamics**: Heterogeneous payoff distributions and contributions can promote cooperation. Nonlinear benefit functions and strategic complexity, such as conditional cooperation and the presence of loners, also influence the evolution of cooperation. 3. **Complex Networks**: Social heterogeneity, characterized by degree distribution and clustering, significantly affects the evolution of cooperation. Heterogeneous networks enable complete cooperator dominance at lower values of the synergy factor compared to regular networks. Degree correlations and the presence of hubs play crucial roles in promoting cooperation. 4. **Bipartite Graphs**: To better capture the structure of real-world networks, bipartite graphs are used to account for both pairwise ties and group structures. This approach helps in understanding the impact of group size and composition on cooperation. The review concludes by discussing the challenges and open questions in the field, emphasizing the need for further research to fully understand the dynamics of group interactions in complex systems.