From genotypes to organisms: State-of-the-art and perspectives of a cornerstone in evolutionary dynamics

•Understanding of how genotypes map onto molecular phenotypes and organismal functions is partial.•The networked organization of genotype-phenotype (GP) maps conditions evolution and adaptation.•Several topological properties of genotype spaces are universal.•The evolution of GP maps (not on GP maps) drives the emergence of phenotypes at the species level.•Technical advances permit the exhaustive empirical characterization of small GP maps. Understanding how genotypes map onto phenotypes, fitness, and eventually organisms is arguably the next major missing piece in a fully predictive theory of evolution. We refer to this generally as the problem of the genotype-phenotype map. Though we are still far from achieving a complete picture of these relationships, our current understanding of simpler questions, such as the structure induced in the space of genotypes by sequences mapped to molecular structures, has revealed important facts that deeply affect the dynamical description of evolutionary processes. Empirical evidence supporting the fundamental relevance of features such as phenotypic bias is mounting as well, while the synthesis of conceptual and experimental progress leads to questioning current assumptions on the nature of evolutionary dynamics—cancer progression models or synthetic biology approaches being notable examples. This work delves with a critical and constructive attitude into our current knowledge of how genotypes map onto molecular phenotypes and organismal functions, and discusses theoretical and empirical avenues to broaden and improve this comprehension. As a final goal, this community should aim at deriving an updated picture of evolutionary processes soundly relying on the structural properties of genotype spaces, as revealed by modern techniques of molecular and functional analysis.