In the present talk, experimental and theoretical work relative to transport through split gate quantum dot structures in GaAs and Si is discussed. Nonlinear transport is studied through split gate GaAs/AlGaAs heterostructure quantum dots, where deviations are observed of the current voltage (I-V) characteristics from that expected from the standard Landauer-Büttiker model. In some quantum dot samples, this leads to S-type negative differential conductance (SNDC) with corresponding bistable behavior. Otherwise, deviations in the ideal conductance are observed as a 'kink' in the I-V close to the threshold for conduction, which is observed in simple quantum point contacts (QPCs) as well. This behavior in QPCs is also found to be correlated with the onset of time dependent random telegraph noise close to threshold. Possible explanations in terms of carrier heating phenomena and charge instabilities are discussed. Transport measurements are also presented on a novel double gate, split-gate Si MOS quantum dot structures with controllable 2DEG density. Strong oscillations in the linear conductance through the dot are observed as a function of both the top-gate and side-gate bias. An overall monotonic and quasi-periodic movement of the peak conductance is observed which is believed to be associated with the bare level structure of the electronic states in the dot coupled with the Coulomb charging energy. In addition, an apparent level splitting is observed in many regions as well as a second period in the peak conductance, suggestive of level degeneracy breaking and possible multi-particle effects. The overall behavior is compared with theoretical self-consistent solutions of the coupled 3D Schrödinger-Poisson equations for the same geometry, where the overall peak behavior with top and side gate bias appear to be well correlated with the voltage dependence of the calculated bare energy spacing in the dot from such self-consistent calculations.