Fluid–fluid interfaces, laden with polymers, particles or other surface-active moieties, often show a rheologically complex response to deformations, in particular when strong lateral interactions are present between these moieties. The response of the interface can then no longer be described by an isotropic surface tension alone. These “structured” soft-matter interfaces are found in many industrial applications, ranging from foods, cosmetics and pharmaceuticals, to oil recovery. Also many biomedical applications involve such interfaces, including those involving lung surfactants and biofilms. In order to understand, design and optimize processes in which structured interfaces are present, flow predictions of how such multiphase systems deform are of the utmost importance, which is the goal of “computational interfacial rheology”, the main topic of this review. We start by rigorously establishing the stress boundary condition used in the computation of multi-phase flows, and show how this changes when the interface is rheologically complex. Then, constitutive models for the extra stress in interfaces, ranging from 2D generalized Newtonian to hyperelastic and viscoelastic, are reviewed extensively, including common pitfalls when applying these models. This is followed by an overview of different approaches to measure interfacial rheological properties, and a discussion of advanced numerical implementations for deforming interfaces. We conclude with an outlook for this relatively young and exciting field.