Observations of Galactic dust are a highlight and a lasting legacy of the Planck space mission. Spectacular images combining the intensity of dust emission with the texture derived from polarization data have received world-wide attention and become part of the general scientific knowledge. Beyond this popular success, the dust maps are an immense step forward for Galactic astrophysics, greatly superseding earlier observations. Planck has provided us with the data needed to statistically characterize the structure of the Galactic magnetic field and its coupling with interstellar matter and turbulence. Planck multi-frequency observations have also opened a new perspective on interstellar dust, upsetting existing models. Futrhermore, the astrophysics of dust emission has become inter-connected to a paramount objective of observational cosmology: the quest for curl-like (B-mode) polarization of the cosmic microwave background expected to arise from primordial gravitational waves produced during the inflation era in the very early Universe. I will introduce these science topics and highlight key results and perspectives of on-going research.