Lateral flow immunoassay (LFIA), as a well-known point-of-care testing (POCT) technique, is of vital significance in a variety of application scenarios due to the advantages of convenience and high efficiency. With rapid development of computational intelligence (CI), algorithms have played an important role in enhancing LFIA performance, and it is necessary to summary how algorithms can assist LFIA improvement for providing experiences. However, most existing works on LFIA are from biochemical field which pay more attention to material and reagent. Therefore, in this paper, a systematical survey is proposed to review works on applying mathematical tools to promote LFIA development. Particularly, a novel two-level taxonomy is designed for a better inspection, including LFIA-oriented mathematical modelling, CI-assisted post-processing and quantification in LFIA, and each level is further subdivided for in-depth understanding. In addition, from a higher viewpoint, outlooks of jointly developing POCT with other state-of-the-art techniques are presented from perspectives of implementation principle, technical approach and algorithm application. Moreover, this survey aims to highlight that applying CI methods is competent for boosting POCT development, so as to raise attentions from more areas like information science, extend deeper researches and inspire more interdisciplinary works.