Claudins are one of the major components of tight junctions (TJs) that polymerize within the cell membrane and form interactions between cells. Some claudins seal the paracellular space, limiting paracellular flux, while others form selectively permeable ion channels that control the paracellular permeability of small ions. Claudin strands are known to be dynamic and reshape within TJs to accommodate large-scale movements and rearrangements of epithelial tissues. Here, we summarize the recent computational and modeling studies on claudin assembly into tetrameric ion channels and their polymerization into μm long strands within the membrane. Computational studies ranging from all-atom molecular dynamics, coarse-grained simulations, and hybrid-resolution simulations elucidate the molecular nature of claudin assembly and function and provide a framework that describes the lateral flexibility of claudin strands.