Abstract: Compared with one-dimensional (1D) and three-dimensional (3D) polymers, the theory framework of two-dimensional (2D) polymers is still incomplete, especially for flexible 2D polymers. Their unique conformation and properties are one of the mysterious questions in the polymer science. This article comprehensively reviews the theoretical and simulation research progress of flexible 2D polymers, aiming to systematically sort out the development of the field of flexible 2D polymers from early theoretical prototypes to recent conformational physics research. First, this article reviews theoretical research on tethered membranes from the 1980s. Early molecular dynamics simulations revealed that self-avoidance causes 2D networks to approach a flat state at the thermodynamic limit, rather than undergoing a crumpled transition. Second, the article elaborates on the breakthroughs achieved in theory and simulation since the 21st century: (1) systematically studied, through simulation, the correlation between the equilibrium morphology of 2D polymer sheets and their transport properties, and validated the theoretical relationship between intrinsic viscosity [η] and the scaling exponent v; (2) By introducing a 2D network model with adjustable grid size, the long-standing controversial flat and crumpled conformations were theoretically unified, finding that the two can coexist in the same system, and their conformations depend on the network size and grid size; (3) The folding behavior of flexible 2D polymers in different solvents was systematically studied, and the transition rules from flat to multi-level folding to collapsed were discovered, and the corresponding theoretical model was established.

Key words: Two-dimensional polymer, Flexible, Conformation, Scaling relations