Knowledge of both prokaryotic and eukaryotic organisms is essential to the study of molecular evolution. Their common ancestry mandates that their molecular functions share many aspects of adaptation and constraint, yet their differences in size, ploidy, and structural complexity also give rise to divergent evolutionary options. We explore the interplay of adaptation, constraint, and neutrality in their evolution by the use of genetic variants to probe molecular function in context of molecular structure, metabolic organization, and phenotype-environment interactions. Case studies ranging from bacteria to butterflies, flies, and vertebrates emphasize, among other points: the importance of moving from initial recording of evolutionary pattern variation to studying the processes underlying the patterns, by experiment, reconstructive inference, or both; the complementarity, not conflict, of finding different performance and fitness impacts of natural variants in prokaryotes or eukaryotes, depending on the nature and magnitude of the variants, their locations and roles in pathways, the nature of molecular function affected, and the resulting organismal phenotype-environment interactions leading to selection or its absence; the importance of adaptive functional interaction of different kinds of variants, as in gene expression variants versus variants altering polypeptide properties, or interaction of changes in enzymes' active sites with complementary changes elsewhere that adjust catalytic function in different ways, or coadaptation of different steps' properties in pathways; the power afforded by combining structural and functional analyses of variants with study of the variants' phenotype-environment interactions to understand how molecular changes affect (or fail to affect) adaptive mechanisms "in the wild." Comparative study of prokaryotes and eukaryotes in this multifaceted way promises to deliver both new insights into evolution and a host of new and productive questions about it.