In this talk, we will first review the Peskin problem in 2-D, and then introduce the so-called tangential Peskin problem with a novel Eulerian perspective. We prove existence of its global weak solution for arbitrary non-negative initial data in the energy class satisfying some natural conditions. This is considered as a super-critical problem in the existing studies with Lagrangian perspectives. Regularity and long-time behavior of the constructed solution is established, and uniqueness is proved under additional assumptions. Further implications of these results will also be discussed.