  We highlight the current state-of-the-art in modeling emulsion rheology,
ranging from dilute to jammed dense systems. We focus on analytical and
numerical methods developed for calculating, computing, and tracking drop
deformation en route to developing constitutive models for flowing emulsions.
We identify material properties and dimensionless parameters, collate the small
deformation theories and resulting expressions for viscometric quantities, list
theoretical and numerical methods, and take stock of challenges for capturing
connections between drop deformation, morphology, and rheology of emulsions. We
highlight the substantial progress in providing quantitative descriptions of
the rheological response using analytical theories, dimensional analysis, and
powerful computational fluid dynamics to determine how macroscopic rheological
properties emerge from microscopic features, including deformation and dynamics
of non-interacting or interacting drops and molecular aspects that control the
interfacial properties.
