An image line segment is a fundamental low-level visual feature that delineates straight, slender, and uninterrupted portionsof objects and scenarios within images. Detection and description of line segments lay the basis for numerous vision tasks. Althoughmany studies have aimed to detect and describe line segments, a comprehensive review is lacking, obstructing their progress. This studyfills the gap by comprehensively reviewing related studies on detecting and describing two-dimensional image line segments to provideresearchers with an overall picture and deep understanding. Based on their mechanisms, two taxonomies for line segment detectionand description are presented to introduce, analyze, and summarize these studies, facilitating researchers to learn about them quicklyand extensively. The key issues, core ideas, advantages and disadvantages of existing methods, and their potential applications for eachcategory are analyzed and summarized, including previously unknown findings. The challenges in existing methods and correspondinginsights for potentially solving them are also provided to inspire researchers. In addition, some state-of-the-art line segment detectionand description algorithms are evaluated without bias, and the evaluation code will be publicly available. The theoretical analysis, coupledwith the experimental results, can guide researchers in selecting the best method for their intended vision applications. Finally, this studyprovides insights for potentially interesting future research directions to attract more attention from researchers to this field.