Numerous behavioral studies suggest that the processing of various types of visual stimuli and features may be more efficient in either the left or the right visual field. However, not all of these visual-field asymmetries (VFAs) have been observed consistently. Moreover, it is typically unclear whether a failure to observe a particular VFA can be ascribed to certain characteristics of the participants and stimuli, to a lack of statistical power, or to the actual absence of an effect. To increase our understanding of lateralization of visual information processing, we have taken a rigorous methodological and statistical approach to examine the reproducibility of various previously reported VFAs. We did so by performing (near-)exact replications of nine representative previous studies, aiming for sufficient power to detect the effects of interest, and taking into consideration all relevant dependent variables (reaction times and error rates). Following Bayesian analyses –on our data alone as well as on the combined evidence from the original and replication studies– we find precise and reliable evidence that support VFAs in the processing of faces, emotional expressions, global and local information, words, and in the distribution of spatial attention. In contrast, we find less convincing evidence for VFAs in processing of high and low spatial frequencies. Finally, we find no evidence for VFAs in categorical perception of color and shape oddballs, and in the judgments of categorical and coordinate spatial relations. We discuss our results in the light of their implications for theories of visual lateralization.