  To offer a view into the rapidly developing theory of fractional diffusion
processes we describe in some detail three topics of present interest: (i) the
well-scaled passage to the limit from continuous time random walk under power
law assumptions to space-time fractional diffusion, (ii) the asymptotic
universality of the Mittag-Leffler waiting time law in time-fractional
processes, (iii) our method of parametric subordination for generating particle
trajectories.
