Intracellular organelles, including secretory vesicles, emerged when eukaryotic cells evolved some 3 billion years ago. The primordial organelles that evolved in Archaea were similar to endolysosomes, which developed, arguably, for specific metabolic tasks, including uptake, metabolic processing, storage and disposal of molecules. In comparison with prokaryotes, cell volume of eukaryotes increased by several orders of magnitude and vesicle traffic emerged to allow for communication between distant intracellular locations. Lysosomes, first described in 1955, a prominent intermediate of endo- and exocytotic pathways, operate virtually in all eukaryotic cells including astroglia, the most heterogeneous type of homeostatic glia in the central nervous system. Astrocytes support neuronal network activity in particular through elaborated secretion, based on a complex intracellular vesicle network dynamics. Deranged homeostasis underlies disease and astroglial vesicle traffic contributes to the pathophysiology of neurodegenerative (Alzheimer's disease, Huntington's disease), neurodevelopmental diseases (intellectual deficiency, Rett's disease) and neuroinfectious (Zika virus) disorders. This review addresses astroglial cell-autonomous vesicular traffic network, as well as its into primary and secondary vesicular network defects in diseases, and considers this network as a target for developing new therapies for neurological conditions.