Background Recent work has revealed that many biological systems keep functioning in the face of mutations and therefore can be considered genetically robust. However, several issues related to robustness remain poorly understood, such as its implications for evolvability (the ability to produce adaptive evolutionary innovations). Results Here, we use the Avida digital evolution platform to explore the effects of genetic robustness on evolvability. First, we obtained digital organisms with varying levels of robustness by evolving them under combinations of mutation rates and population sizes previously shown to select for different levels of robustness. Then, we assessed the ability of these organisms to adapt to novel environments in a variety of experimental conditions. The data consistently support that, for simple environments, genetic robustness fosters long-term evolvability, whereas, in the short-term, robustness is not beneficial for evolvability but may even be a counterproductive trait. For more complex environments, however, results are less conclusive. Conclusion The finding that the effect of robustness on evolvability is time-dependent is compatible with previous results obtained using RNA folding algorithms and transcriptional regulation models. A likely scenario is that, in the short-term, genetic robustness hampers evolvability because it reduces the intensity of selection, but that, in the long-term, relaxed selection facilitates the accumulation of genetic diversity and thus, promotes evolutionary innovation.