The first steps of planet formation are believed to be the growth of initially
small, micrometric dust grains and their decoupling from
the gas phase via vertical settling and radial migration. With the advent of
ALMA and extreme adaptive optics system, such as VLT/SPHERE, it is now possible
to probe the dust in discs at resolutions of about 0.05 arsec. In this talk, I
will present a few recent results that allow us to put quantitative constraints
on the evolution of dust grain and on the mechanisms of planet formation.
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