The Third Generation Partnership Project (3GPP) was established to bring together several standards organization to address the needs related to the specification of mobile broadband. Originally targeting the evolution from 2G to 3G, 3GPP continues at the forefront of the standardization effort leading to 5G and beyond. Given the growing diversity of services and the explosion of mobile users year by year, evolving architectures have then been successively proposed by the group in order to expand the limits of legacies systems. We overview this evolution, summarizing the transformation of core systems and their related decomposition, aggregation, and mapping operations from 3G to 5G systems. We also present an in-depth description of 5G Core based on recent technical documents delivered by 3GPP. We end with the identification of potential operational and technical challenges in 5G systems.