Understanding deformations during interaction of colloidal or nano droplets. has important implications in a wide range of applications such as flotation collection and emulsion stability. The present work is important and necessary because current models are unable to properly describe recent experimental results obtained using the Atomic Force Microscope (AFM) and Surface Force Apparatus (SFA). We revisit and improve on theories involving interacting deformable droplets. A detailed theoretical model of the experiments, which accounts for surface forces, hydrodynamic interactions, droplet deformation and AFM cantilever detection, has been developed. The new feature of the model is the use of matched asymptotic expansions to derive a new boundary condition at constant volume to obtain results that are independent of the size of the computational domain. The AFM experiments provide measurements of dynamical forces between two interacting droplets as well as between a drop and a colloidal particle of micrometre radii in solution when they are driven together and then are retracted from each other. The SFA experiments measure (time dependent) surface profiles of a millimetre size mercury drop interacting with a mica surface. Different configurations have been studied including mechanical and electrical perturbations to a thin film stabilized by double layer repulsion. Interesting experimental features were observed when approaching or retracting the mica from the mercury drop.