Abstract: Semantic communication has attracted considerable interest because of its potential to support emerging human-centric services such as holographic communications， extended reality （XR）， and human-machine interactions. Contrary to traditional communication systems that focus on minimizing symbol-level distortion （e.g.， bit error rate and signal-to-noise ratio）， semantic communication targets delivering the intended meaning to the destination user， which is often quantified by various statistical divergences referred to as semantic distances. However， there remains a lack of a unified theoretical framework for semantic communication that can quantify the rate-distortion tradeoff when different task-specific semantic distance metrics are employed. To address this gap， we propose a task-oriented semantic rate-distortion theory， which is compatible with multiple task-dependent divergence measures. To investigate the impact of different semantic distance metrics on achievable rates， case studies were conducted on two representative tasks， classification and signal generation， and their performances were compared under various scenarios. The result analysis revealed the fundamental trade-offs between rate， distortion， and semantic distance in semantic communication.