Sentence semantic matching requires an agent to determine the semantic relation between two sentences, which is widely used in various natural language tasks, such as Natural Language Inference (NLI), Paraphrase Identification (PI), and so on. Much recent progress has been made in this area, especially attention-based methods and pre-trained language model based methods. However, most of these methods focus on all the important parts in sentences in a static way and only emphasize how important the words are to the query, inhibiting the ability of attention mechanism. In order to overcome this problem and boost the performance of attention mechanism, we propose a novel dynamic re-read attention, which can pay close attention to one small region of sentences at each step and re-read the important parts for better sentence representations. Based on this attention variation, we develop a novel Dynamic Re-read Network (DRr-Net) for sentence semantic matching. Moreover, selecting one small region in dynamic re-read attention seems insufficient for sentence semantics, and employing pre-trained language models as input encoders will introduce incomplete and fragile representation problems. To this end, we extend DRrNet to Locally-Aware Dynamic Re-read Attention Net (LadRa-Net), in which local structure of sentences is employed to alleviate the shortcoming of Byte-Pair Encoding (BPE) in pre-trained language models and boost the performance of dynamic reread attention. Extensive experiments on two popular sentence semantic matching tasks demonstrate that DRr-Net can significantly improve the performance of sentence semantic matching. Meanwhile, LadRa-Net is able to achieve better performance by considering the local structures of sentences. In addition, it is exceedingly interesting that some discoveries in our experiments are consistent with some findings of psychological research.