We theoretically investigate the effect of the lead dimensionality on the non-equilibrium electron transport through quantum dots. More precisely, we study nonlinear transport in a quantum dot coupled to leads of diverse dimensionality. We show that the presence of the latter strongly determines the resulting transport properties. Differently from higher dimensional leads (wide and smooth band limit), van Hove singularities in the density of states of low-dimensional reservoirs determine sharp resonances in the differential conductance at finite applied voltages as well as in the dot spectral density. It is also shown that, due to the finiteness of the terminal bandwidth, the differential conductance change its sign at higher biases. These results clearly indicate that the environment does play an important role in determining transport properties in mesoscopic systems.