This chapter contains sections titled: Introduction An Outline of the Gnedenko–Kovalenko Theory of Thinning The Continuous Time Random Walk (CTRW) Manipulations: Rescaling and Respeeding Power Laws and Asymptotic Universality of the Mittag-Leffler Waiting-Time Density Passage to the Diffusion Limit in Space The Time-Fractional Drift Process Conclusions References