Spectral sequence calculation for unstable $v_n$-periodic homotopy groups of spheres.
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Besides reviewing historical development and prerequisites, we present the main ingredients needed for calculations with spectral sequences for this purpose. These include the Bousfield-Kuhn functor, the Goodwillie tower and so on. We then outline current approaches to running such spectral sequences from cohomology to homotopy, as well as indicate specific questions to investigate.