The emergence of graphene and two-dimensional van der Walls materials renewed interest to investigation of the low-frequency noise in the low-dimensional systems. The layered van der Waals materials offers unique opportunities for studying the low-frequency noise owing to the properties controlled by the thickness of these materials, and tunable carrier concentration. In this review, we describe unusual low-frequency noise phenomena in quasi-2D and quasi-1D van der Waals materials. We also demonstrate that the low-frequency noise spectroscopy is a powerful tool for investigation of the electron transport and charge-density-wave phase transitions in this class of materials.