Malignant glioma cells invade the surrounding brain parenchyma, by migrating along the blood vessels, thus promoting cancer growth. The biological bases of these activities are grounded in profound alterations of the metabolism and the structural organization of the cells, which consequently acquire the ability to modify the surrounding microenvironment, by altering the extracellular matrix and affecting the properties of the other cells present in the brain, such as normal glial-, endothelial- and immune-cells. Most of the effects on the surrounding environment are probably exerted through the release of a variety of extracellular vesicles (EVs), which contain many different classes of molecules, from genetic material to defined species of lipids and enzymes. EV-associated molecules can be either released into the extracellular matrix (ECM) and/or transferred to neighboring cells: as a consequence, both deep modifications of the recipient cell phenotype and digestion of ECM components are obtained, thus causing cancer propagation, as well as a general brain dysfunction. In this review, we first analyze the main intracellular and extracellular transformations required for glioma cell invasion into the brain parenchyma; then we discuss how these events may be attributed, at least in part, to EVs that, like the pawns of a dramatic chess game with cancer, open the way to the tumor cells themselves.