If If ϕ is a one-variable inner function, then one can use its model space (H2(𝔻)⊖ϕH2(𝔻)) to build a realization of ϕ. This is roughly a useful way of representing ϕ using operators related to its model space. In this one-variable setting, the realization naturally inherits some regularity properties of ϕ. This talk is concerned with realizations of two-variable inner functions ϕ on the bidisk 𝔻^2 built from the associated two variable model spaces (H2(𝔻^2)⊖ϕH2(𝔻^2)). We’ll look at some concrete formulas for general inner functions and refined results for a special class of inner functions called quasi-rational. Time-permitting, we'll discuss an application to matrix monotonicity and some open questions. This is joint work with J.E. Pascoe and Ryan Tully-Doyle.