Semantic processing is a fundamental research domain in computational linguistics. In the era of powerful pre-trained language models and large language models, the advancement of research in this domain appears to be decelerating. However, the study of semantics is multi-dimensional in linguistics. The research depth and breadth of computational semantic processing can be largely improved with new technologies. In this survey, we analyzed five semantic processing tasks, e.g., word sense disambiguation, anaphora resolution, named entity recognition, concept extraction, and subjectivity detection. We study relevant theoretical research in these fields, advanced methods, and downstream applications. We connect the surveyed tasks with downstream applications because this may inspire future scholars to fuse these low-level semantic processing tasks with high-level natural language processing tasks. The review of theoretical research may also inspire new tasks and technologies in the semantic processing domain. Finally, we compare the different semantic processing techniques and summarize their technical trends, application trends, and future directions.