An experimental study of drop dynamics under shear is conducted for five fluid pairs: a reference Newtonian system, two systems with a viscoelastic drop in a Newtonian matrix, one with a Newtonian drop in a viscoelastic matrix, all at drop to matrix viscosity ratio ¿=1.5¿=1.5, and a separate case at ¿=0.75¿=0.75. The viscoelastic liquids are either a Boger fluid or a shear-thinning viscoelastic fluid satisfying an Ellis model. Deborah numbers in the range 1–2 and a range of capillary numbers from low to above breakup conditions are addressed. The results focus on three aspects: relaxation after cessation of shear, a new viscoelastic drop breakup scenario, and the effect of shear flow history on drop breakup. Numerical simulations with the 3D volume-of-fluid PROST method complement the experimental results.