In the past years, there has been a growing interest in innovative applications of radially polarized laser beams. Among them, the particular field of laser-driven electron acceleration has received much attention. Recent developments in high-power infrared laser sources at the INRS Advanced Laser Light Source (Varennes, Qc, Canada) allowed the experimental observation of a quasi-monoenergetic 23-keV electron beam produced by a radially polarized laser pulse tightly focused into a low density gas. Theoretical analyses suggest that the production of collimated attosecond electron pulses is within reach of the actual technology. Such an ultrashort electron pulse source would be a unique tool for fundamental and applied research. In this paper, we propose an overview of this emerging topic and expose some of the challenges to meet in the future.