Transient and steady deformation of a single Newtonian drop immersed in a non-Newtonian matrix subjected to a homogeneous shear flow is investigated microscopically. Two model Boger fluids have been used as non-Newtonian matrices. The three-dimensional drop shape is completely determined as observations from both the velocity-vorticity and velocity-velocity gradient plane are available. Start-up and relaxation are investigated varying both the capillary number and the elasticity of the matrix fluid, while the viscosity ratio is kept constant. The extensive data set demonstrates that matrix elasticity reduces the steady drop deformation and promotes droplet orientation, can induce a drop deformation overshoot in the start-up experiments and slows down the relaxation phenomena. The experimental results have been compared with predictions of a phenomenological model [M. Minale, J. Non-Newtonian Fluid Mech. 123, 151-160 (2004)], that is slightly modified in the present work. It shows good agreement with the experimental data up to moderate capillary numbers (Ca approximate to 0.2). For higher Ca, the observed trends are still correctly predicted, although quantitative agreement is less satisfying. A systematic deviation is observed at the end of the relaxation process. This result, together with a systematic, quantitative discrepancy in the experimental data between the two Boger fluids, suggests that the underlying rheological model is probably too simplistic to allow a quantitative prediction of all effects caused by matrix elasticity. (c) 2007 The Society of Rheology.