The origin and evolution of modern biochemistry and cellular structure is a complex problem that has puzzled scientists for almost a century. While comparative, functional and structural genomics has unraveled considerable complexity at the molecular level, there is very little understanding of the origin, evolution and structure of the molecules responsible for cellular or viral features in life. Recent efforts, however, have dissected the emergence of the very early molecules that populated primordial cells. Deep historical signal was retrieved from a census of molecular structures and functions in thousands of nucleic acid and protein structures and hundreds of genomes using powerful phylogenomic methods. Together with structural, chemical and cell biology considerations, this information reveals that modern biochemistry is the result of the gradual evolutionary appearance and accretion of molecular parts and molecules. These patterns comply with the principle of continuity and lead to molecular and cellular complexity. Here, we review findings and report possible origins of molecular and cellular structure, the early rise of lipid biosynthetic pathways and components of cytoskeletal microstructures, the piecemeal accumulation of domains in ATP synthase complexes and the origin and evolution of the ribosome. Phylogenomic studies suggest the last universal common ancestor of life, the ‘urancestor', had already developed complex cellular structure and bioenergetics. Remarkably, our findings falsify the existence of an ancient RNA world. Instead they are compatible with gradually coevolving nucleic acids and proteins in interaction with increasingly complex cofactors, lipid membrane structures and other cellular components. This changes the perception we have of the rise of modern biochemistry and prompts further analysis of the emergence of biological complexity in an ever-expanding coevolving world of macromolecules.