Abstract: Our present knowledge of the translational mobility of guest molecules in zeolites would be unthinkable without the involvement of the giant zeolite crystallites synthesized by Prof. Sergey Petrovich Zhdanov in Leningrad. The present contribution narrates how the availability of his “tailor-made” zeolite samples, jointly with the potentials of the pulsed field gradient nuclear magnetic resonance (PFG NMR) allowed, for the very first time, the direct measurement of molecular displacements within the interior of zeolite crystals and, thus, of zeolitic guest diffusion. Starting with an introduction into the potentials of PFG NMR diffusion measurements quite in general, the paper reports about the hidden pitfalls, which by recording molecular uptake and release in conventional diffusion measurements may lead to substantial inconsistencies, and about their elucidation via PFG NMR owing to Zhdanov’s giant zeolites. A survey of the main achievements of diffusion studies by PFG NMR with Zhdanov’s zeolites is given. It ranges from knowledge about the different patterns of the concentration dependencies of diffusion via diffusion in multicomponent systems including chemical reactions up to the exploration of hierarchies of diffusion resistances. The review is concluded by highlights of most recent diffusion studies including “nanoscopic” diffusion measurement via deuterium NMR and the message of purposefully designed conversion studies on mass transfer.