Fully-developed flow and heat transfer in periodic converging-diverging channels with rectangular cross sections are studied using computational fluid dynamics (CFD) simulations for Reynolds numbers ranging from 50 to 200. Experimental laser sheet flow visualizations have also been utilized with the aid of an enlarged transparent Perspex model, which serves as a form of secondary verification of the CFD results. The CFD investigations focus on two principal configurations of converging-diverging channels, namely the constant curvature and sinusoidal converging-diverging channel. Heat transfer simulations have been carried out under constant wall temperature conditions using liquid water as the coolant. It is found that due to the fluid mixing arising from a pair of recirculating vortices in the converging-diverging channels, the heat transfer performance is always significantly more superior to that of straight channels with the same average cross sections; at the same time the pressure drop penalty of the converging-diverging channels can be much smaller than the heat transfer enhancement. The effects of channel aspect ratio and amplitude of the converging-diverging profiles have been systematically investigated. The results show that for a steady flow, the flow pattern is generally characterized by the formation of a pair of symmetrical recirculating vortices in the two furrows of the converging-diverging channel. Both the optimal aspect ratio and channel amplitude are being presented with the support of CFD analyses. Experimental flow visualizations have also been utilized and it was found that the experimental results agrees favorably with the CFD results. The present study shows that these converging-diverging channels have prominent advantages over straight channels. The most superior configuration considered in this paper has been found to yield an improvement of up to 60% in terms of the overall thermal-hydraulic performance compared to microchannels with straight walls, thus serving as promising candidates for incorporation into efficient heat transfer devices.