This dissertation reports results of an investigation of electron transport in two classes of layered van der Waals materials: quasi-one-dimensional (1D) transition metal trichalcogenides (TMTs) and quasi-two-dimensional (2D) transition metal dichalcogenides (TMDs). Practical motivations for this study include the search for (i) materials, which can be used in ultimately downscaled interconnects in the next generations of electronics, and (ii) materials revealing low power switching phenomena, which can be used in future logic circuits. TMTs have strong covalent bonds in one direction and weaker bonds in cross-plane directions. They can be prepared as crystalline nanoribbons consisting of 1D atomic threads, i.e. chains. I have examined the current carrying capacity of ZrTe3 nanoribbons using structures fabricated by the shadow mask method. It was found that ZrTe3 nanoribbons reveal an exceptionally high current density, on the order of ~100 MA/cm2, at the peak of the stressing current. I have investigated the low-frequency electronic noise in such nanoribbons. The low-frequency noise data were used to determine the activation energy for electromigration. TMDs reveal interesting charge-density-wave (CDW) effects, which can be triggered by electric bias even at various temperatures. I investigated switching among three CDW phases – commensurate, nearly commensurate, incommensurate – and the normal metallic phase in 1T-TaS2 devices induced by application of an in-plane bias voltage. The switching among all phases was achieved over a wide temperature range, from 77 K to 400 K. The electronic noise spectroscopy was used as an effective tool for monitoring the transitions. The noise exhibits sharp increases at the phase transition points, which correspond to the step-like changes in resistivity. The possibility of the bias-voltage switching among four different phases of 1T-TaS2 is a promising step toward nanoscale device applications. The results also demonstrate the potential of noise spectroscopy for investigating and identifying phase transitions in the materials.