Is evolution predictable at the molecular level? The ambitious goal to answer this question requires an understanding of the mutational effects that govern the complex relationship between genotype and phenotype. In practice, it involves integrating systems-biology modelling, microbial laboratory evolution experiments and large-scale mutational analyses - a feat that is made possible by the recent availability of the necessary computational tools and experimental techniques. This Review investigates recent progresses in mapping evolutionary trajectories and discusses the degree to which these predictions are realistic.