Cosmic dust plays a key role in the evolution of galaxies and is known to obscure the bulk of cosmic star formation out to at least redshift 4. However, in order to determine the importance of dust at higher redshifts — in particular in the epoch of reionization — deep ALMA observations of a large number of galaxies are crucial. The ALMA Large Program REBELS provides the first such sample by targeting 40 UV-selected galaxies at z > 6.5 in dust continuum and [CII] emission. In this talk, I will show that dust is common among the REBELS sample, and that dust-obscured star formation therefore still contributes significantly to the total cosmic star formation rate density at z~7. In addition, by making use of recently carried out ALMA observations in Band 8, I will discuss new dust temperature measurements of three REBELS targets, and the corresponding implications for dust production in the early Universe.