Many genes have nycthemeral rhythms of expression, i.e. a 24-hours periodic variation, at either mRNA or protein level or both, and most rhythmic genes are tissue-specific. Here, we investigate and discuss the evolutionary origins of rhythms in gene expression. Our results suggest that rhythmicity of protein expression could have been favored by selection to minimize costs. Trends are consistent in bacteria, plants and animals, and are also supported by tissue-specific patterns in mouse. Unlike for protein level, cost cannot explain rhythm at the RNA level. We suggest that instead it allows to periodically reduce expression noise. Noise control had the strongest support in mouse, with limited evidence in other species. We have also found that genes under stronger purifying selection are rhythmically expressed at the mRNA level, and we propose that this is because they are noise sensitive genes. Finally, the adaptive role of rhythmic expression is supported by rhythmic genes being highly expressed yet tissue-specific. This provides a good evolutionary explanation for the observation that nycthemeral rhythms are often tissue-specific.