We investigate the behaviour of dust in protoplanetary disks under the action of gas drag using our 3D, two-fluid (gas+dust) SPH code. We present the evolution of the dust spatial distribution in global simulations of planetless disks as well as of disks containing an already formed planet. The resulting dust structures vary strongly with particle size and planetary gaps are much sharper than in the gas phase, making them easier to detect with ALMA than anticipated. We also find that there is a range of masses where a planet can open a gap in the dust layer whereas it doesn't in the gas disk. Our dust distributions are fed to the radiative transfer code MCFOST to compute synthetic images, in order to derive constraints on the settling and growth of dust grains in observed disks.