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The emergence of synchronization and its general features are of particular interest to scientists working on several areas, such as physics, social sciences and biology. From neurons to population dynamics and fireflies, nature showcases several examples of synchronized and collective behavior. The paradigmatic model to investigate synchronization was proposed by Y. Kuramoto in 1975, with several extensions and generalizations being studied in the years that followed. This colloquium aims at overviewing some interesting modifications of this model such as frustration, external forces and higher order interactions, in addition to discussing some fundamental aspects of synchronization phenomena. Finally, I will comment on some contributions from our research group and some prospects on this subject