This chapter outlines several key open problems that remain critical for advancing semantic communication systems. A universal mathematical framework is still lacking, since the notion of semantics depends heavily on context and task. Current approaches also rely on deep learning, which improves efficiency but consumes substantial computing resources, raising the need for lighter models and better integration of cloud, edge, and device computing. Privacy and security pose new risks, as transmitting condensed, high-level features may expose sensitive information. Moreover, ensuring robust performance under dynamic and uncertain conditions remains a key difficulty. Generative models show promise but face challenges in safety, reliability, and evaluation. Finally, high-mobility scenarios demand mobility-aware semantic strategies. Together, these issues define the path toward practical and trustworthy semantic communication in future networks.