Applications of the newly developed hybrid of the boundary integral and economical multipole techniques to large–scale dynamical simulations of concentrated emulsion flows of deformable drops are considered. For N=O(102−103) drops in a periodic cell with O(103) boundary elements per drop, the method has two to three orders of magnitude gain over a standard boundary–integral method at each time–step, thus making long–time large–scale dynamical simulations feasible. In the steady shear flow, large systems N≥O(102) are imperative for convergence at high drop volume fractions c≥0.5. At high concentrations, most of the shear thinning occurs for nearly non–deformed drops; at c≈0.55 and small capillary numbers, phase transition is observed in dynamical simulations. In sedimentation of deformable drops from a homogeneous initial state, even larger N≥O(103) are required to accurately describe the Koch–Shaqfeh type of instability in a wide time range with N up to 1200 and ensemble averaging over the initial conditions. The dynamics of the average sedimentation rate is studied versus concentration c for matching viscosities λ=1; for a Bond number of 1.75, systems with c ∼ 0.25 are found to be most unstable. Additionally, a low drop–to–medium–viscosity ratio system, λ= 0.1, is more unstable than those with λ=0.25 and λ=1. In the third application, buoyancy– or gravity–driven motion of a large bubble/drop through a concentrated emulsion of neutrally buoyant drops is studied by simulations. For a size ratio of two, convergent (box–size independent) results for the bubble/drop settling velocity are obtained in simulations with N≤800.