Weakly-supervised temporal action localization (WSTAL) aims to automatically identify and localize action instances in untrimmed videos with only video-level labels as supervision. In this task, there exist two challenges: (1) how to accurately discover the action categories in an untrimmed video (what to discover); (2) how to elaborately focus on the integral temporal interval of each action instance (where to focus). Empirically, to discover the action categories, discriminative semantic information should be extracted, while robust temporal contextual information is beneficial for complete action localization. However, most existing WSTAL methods ignore to explicitly and jointly model the semantic and temporal contextual correlation information for the above two challenges. In this article, a Semantic and Temporal Contextual Correlation Learning Network (STCL-Net) with the semantic (SCL) and temporal contextual correlation learning (TCL) modules is proposed, which achieves both accurate action discovery and complete action localization by modeling the semantic and temporal contextual correlation information for each snippet in the inter- and intra-video manners respectively. It is noteworthy that the two proposed modules are both designed in a unified dynamic correlation-embedding paradigm. Extensive experiments are performed on different benchmarks. On all the benchmarks, our proposed method exhibits superior or comparable performance in comparison to the existing state-of-the-art models, especially achieving gains as high as 7.2% in terms of the average mAP on THUMOS-14. In addition, comprehensive ablation studies also verify the effectiveness and robustness of each component in our model.