The discovery of glioblastoma stem cells (GSCs) in the 2000s revolutionized the cancer research field, raising new questions regarding the putative cell(s) of origin of this tumor type, and partly explaining the highly heterogeneous nature of glioblastoma (GBM). Increasing evidence has suggested that GSCs play critical roles in tumor initiation, progression, and resistance to conventional therapies. The remarkable oncogenic features of GSCs have generated significant interest in better defining and characterizing these cells and determining novel pathways driving GBM that could constitute attractive key therapeutic targets. While exciting breakthroughs have been achieved in the field, the characterization of GSCs is a challenge and the cell of origin of GBM remains controversial. For example, the use of several cell-surface molecular markers to identify and isolate GSCs has been a challenge. It is now widely accepted that none of these markers is, per se, sufficiently robust to distinguish GSCs from normal stem cells. Finding new strategies that are able to more efficiently and specifically target these niches could also prove invaluable against this devastating and therapy-insensitive tumor. In this review paper, we summarize the most relevant findings and discuss emerging concepts and open questions in the field of GSCs, some of which are, to some extent, pertinent to other cancer stem cells.