Capillary flows are increasingly used in biotechnology, biology, chemistry, energy and space applications. Motivated by these new developments, designs of capillary channels have become more sophisticated. In particular, capillary microsystems often use winding channels for reasons such as compactness, or mixing. The behavior of capillary microflows in curved channels is still underdeveloped. In this work, we investigate this type of behavior. In the case of suspended capillary flows, is shown that the flow profile in the curved section is approximately analogous to that in a rectilinear section. In the case of open U-grooves where inner corners are present, the importance of the turn sharpness and of the presence of capillary filaments is pointed out. For sharp turns, and/or in the presence of precursor capillary filaments, we found the phenomenon that the inner filament precedes the outer filament in the channel. Analysis of the capillary flow in curved channels is performed experimentally using rectangular U-grooves and suspended channels. The experimental observations are compared to Surface Evolver numerical software results.