In the mid 1980s, Pete Bousfield and I constructed certain p-local `telescopic' functors Φn from spaces to spectra, for each prime p, and each n ≥ 1. They are constructed using the full strength of the Nilpotence and Periodicity Theorems of Devanitz-Hopkins-Smith, and have some striking properties that relate the chromatic approach to homotopy theory to infinite loopspace theory.
Recently there have been a variety of new uses of these functors, suggesting that they have a central role to play in calculations of periodic phenomena. Here I offer a guide to their construction, characterization, application, and computation.Homology, Homotopy and Applications, Vol. 10 (2008), No. 3, pp.291-319.