In this thesis, results from numerical simulations and experiments on drops squeezing through constricted capillaries are presented. The purpose is to understand how the capillary number changes how drops are deformed as they pass through constrictions and how long it takes them to do so. The simulations use the Cahn–Hilliard phase-field model and the Stokes equations to simulate both simple and compound drops, which are solved using the finite element method with FEniCS. The numerical implementation is validated using test cases such as the spreading of a viscous drop and the Laplace pressure jump in a drop. For the experiments, simple drops were generated using microfluidics techniques and PDMS- chip manufacturing. Experiments with about 300 drops at low Reynolds numbers are presented. The numerical and experimental results do not initially show good agreement, but when changing the viscosity of the two liquids in the simulations the results become more similar. We discuss some possible reasons why the results are different, including the possibility that the boundary conditions on the drop could have been changed because of the use of surfactants. The transit time for simple and compound drops are found for a range of capillary numbers and numerical results show that as the capillary number is reduced, the way the drops are squeezed through the constriction changes and for sufficiently low capillary numbers both simple and compound drops clog the capillary.