Abstract: Common randomness (CR) is a valuable resource for enhancing the trustworthiness of 6G communication systems. This article highlights the role of CR in improving scalability, security, and resilience in distributed 6G architectures. It provides an overview of information-theoretic two-source models for CR generation and summarizes known capacity results, together with their implications for practical systems under different communication settings, including one-way, two-way, helper-assisted, and interactive scenarios. Furthermore, the article explores CR-assisted secure identification over Gaussian channels as an application and highlights selected open research problems in CR generation for next-generation wireless systems. The article targets researchers and practitioners interested in bridging information-theoretic tools with emerging 6G communication systems.