Until quite recently, punning was merely regarded as a rhetorical device or the play of words. Many studies have been conducted from the perspective of structuralism, pragmatics, aesthetics, etc., while the research on the neural mechanism of this language phenomenon has largely been neglected. With the progress made in nonliteral language research, such as metaphor, humor, idiom, and irony, some researchers began to show renewed interest in the ″outdated″ pun research, especially its cognitive mechanism. Compared with the research on other types of nonliteral language such as metaphor, humor, and irony, the research on the pun processing mechanism is still in its infancy, and related studies on Chinese puns are even hardly seen in the literature. Therefore, it is necessary to review and summarize current findings in this field so as to provide guidance for future studies. Despite the lack of specialized semantic access models for pun processing, some pioneering studies can still be found, borrowing resolution models of lexical ambiguity such as the Exhaustive Access Model, the Selective Access Model, the Ordered Access Model, and the Reordered Access Model. Compared with the other three models, the Reordered Access Model is better supported by current findings. According to this model, the meaning access order of a polysemous word depends on the competition between the context and the word meaning frequency. In the case of a pun, the meaning with a higher frequency will be accessed first since both meanings of a pun are usually equally supported by the pun context. In other words, the two meanings of a pun are not accessed simultaneously but sequentially even though it may happen within a very small time window. Besides the progress made in understanding the semantic accessing process during pun comprehension, new findings are reported on its underpinning neural mechanisms as well. It is well established in the neurological literature that the left hemisphere exhibits advantages in language processing; however, more studies begin to show that the right hemisphere is also actively involved in non-literal language processing, especially in the case of less conventional nonliteral language. Findings from current pun research suggest that even though the left hemisphere shows advantages at the early meaning retrieval stage, the right hemisphere is crucial to the success of semantic-context integration and humor appreciation at the later stage. On the basis of current findings and the Model of Psycholinguistic Hemispheric Incongruity Laughter proposed by McHugh and Buchanan in 2016, we propose a Semantic Access Model and a Neurological Model of Pun Comprehension, hoping to shed some light on future studies. We argue that the salient meaning associated with a pun will be accessed first in both hemispheres; failing to pass the activation threshold, the other less salient meaning cannot yet be accessed. It is only when the language processor realizes that the salient meaning is only partially compatible with the pun context, will the less salient meaning be accessed thanks to the more sparse meaning representation manner in the right hemisphere, which then leads to a blending cognitive status where the two meanings intertwine with each other. Although the current neurological research is still at its emerging stage, far from satisfying in terms of scope and depth, we can still provide readers with some preliminary facts about pun processing. Successful comprehension of a pun and appreciation of its humorous effects hinge on the access to and the retention of two distinct meanings, which is subject to the influence of both the context and the word meaning frequency. At the initial stage, the language-dominant hemisphere (usually the left hemisphere) plays a critical role, while the right hemisphere begins to show its influence at the following semantic-contextual integration stage, which is argued to be crucial to the humor appreciation of puns.