Telescopic stable homotopy theory is an approach to studying the stable homotopy category by decomposing it into atomic periodic pieces, the T(n)-local categories. It is a variant of the approach of chromatic homotopy theory that has the advantage of being richer in information, but is a priori less computable. I will explain some recent advances in understanding the telescopic stable homotopy category, and describe some consequences for this on our overall understanding of homotopy groups of spheres. This talk comes from projects that are joint with Arone, Burklund, Carmeli, Clausen, Hahn, Schlank, and Yanovski.