  The disc surrounding PDS 70, with two directly imaged embedded giant planets,
is an ideal laboratory to study planet-disc interaction. We present
three-dimensional smoothed particle hydrodynamics simulations of the system. In
our simulations, planets, which are free to migrate and accrete mass, end up in
a locked resonant configuration that is dynamically stable. We show that
features observed at infrared (scattered light) and millimetre (thermal
continuum) wavelengths are naturally explained by the accretion stream onto the
outer planet, without requiring a circumplanetary disc around planet c. We
post-processed our near-infrared synthetic images in order to account for
observational biases known to affect high-contrast images. Our successful
reproduction of the observations indicates that planet-disc dynamical
interactions alone are sufficient to explain the observations of PDS 70.
