Molecular phenotypes, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurements. Such phenotypes measure molecular functions and are important targets of natural selection. However, the map between encoding DNA sequences and molecular phenotypes is often too difficult to quantify. This lack of knowledge raises an obvious question: which evolutionary properties of a phenotype are universal, that is, independent of the molecular details? In this talk, I will show that universality is an emerging property of complex phenotypes, which are encoded by multiple genomic loci. I will introduce a non-equilibrium framework for adaptive dynamics of such phenotypes in time-dependent environments, and between co-evolving populations. In time-dependent environments, changes in the environment drive the evolution of the species, but not vice versa. As an example, I will present strong evidence that adaptation dominates the evolution of gene expression levels in Drosophila. Co-evolving populations reciprocally affect the fitness of each other, acting as time-dependent environments with feedback. As an example, I will show evidence of co-adaptation between interacting cellular populations of HIV viruses and the antibody repertoire of a patient over the course of an infection. In particular, I will discuss the conditions for emergence of highly potent broadly neutralizing antibodies, which are now recognized as critical for designing an effective vaccine against HIV.