Growing concentration on the novel information processing technology and low‐cost, flexible materials make the spintronics and organic materials appealing for the future interdisciplinary investigations. Organic spintronics, in this context, has arisen and witnessed great advances during the past two decades owing to the continuous innovative exploitation of the charge‐contained spin polarized current. Albeit with such inspiring facts, charge‐absent spin angular momentum flow, namely pure spin currents (PSCs) are less probed in organic functional solids. In this review, the past exploring journey of PSC phenomenon in organic materials are retrospected, including non‐magnetic semiconductors and molecular magnets. Starting with the basic concepts and the generation mechanism for PSC, the representative experimental observations of PSC in the organic‐based networks are subsequently demonstrated and summarized, by accompanying explicit discussion over the propagating mechanism of net spin itself in the organic media. Finally, future perspectives on PSC in organic materials are illustrated mainly from the material point of view, including single molecule magnets, complexes for the organic ligands framework as well as the lanthanide metal complexes, organic radicals, and the emerging 2D organic magnets.