  Planet formation is thought to occur in discs around young stars by the
aggregation of small dust grains into much larger objects. The growth from
grains to pebbles and from planetesimals to planets is now fairly well
understood. The intermediate stage has however been found to be hindered by the
radial-drift and fragmentation barriers. We identify a powerful mechanism in
which dust overcomes both barriers. Its key ingredients are i) backreaction
from the dust onto the gas, ii) grain growth and fragmentation, and iii)
large-scale gradients. The pile-up of growing and fragmenting grains modifies
the gas structure on large scales and triggers the formation of pressure
maxima, in which particles are trapped. We show that these self-induced dust
traps are robust: they develop for a wide range of disc structures,
fragmentation thresholds and initial dust-to-gas ratios. They are favored
locations for pebbles to grow into planetesimals, thus opening new paths
towards the formation of planets.
