Tight junctions form a barrier to control passive transport of ions and small molecules across epithelia and endothelia. In addition to forming a barrier, some of claudins control transport properties of tight junctions by forming charge- and size-selective ion channels. It has been suggested claudin monomers can form or incorporate into tight junction strands to form channels. Resolving the crystallographic structure of several claudins in recent years has provided an opportunity to examine structural basis of claudins in tight junctions. Computational and theoretical modeling relying on atomic description of the pore have contributed significantly to our understanding of claudin pores and paracellular transport. In this paper, we review recent computational and mathematical modeling of claudin barrier function. We focus on dynamic modeling of global epithelial barrier function as a function of claudin pores and molecular dynamics studies of claudins leading to a functional model of claudin channels.