The telescope conjecture has been formulated in stable homotopy theory by Bousfield and Ravenel, and later by Neeman for compactly generated triangulated categories. I will report on recent progress: The conjecture has been established in joint work with Benson and Iyengar for the stable category of representations of any finite group. Also, the conjecture holds for the derived category of any hereditary algebra by a joint result with Stovicek.