Although natural selection is one of the more powerful forces in the biological world, it is not all powerful. The laws of population genetics, biophysics, and biochemistry ultimately define the paths that are open to evolution in different phylogenetic lineages.  However, a large remaining hole in our understanding of evolutionary mechanisms resides at the cellular level. Three vignettes will illustrate recent progress in this area, and most notably how a great deal of evolution at the cellular level is governed by nonadaptive mechanisms. First, I will consider one of the great mysteries of molecular biology – the evolution of diverse multimeric states of proteins, which is completely disassociated with the level of organismal complexity. Second, I will consider the changes in cellular bioenergetic capacity that exist across the prokaryotic-eukaryotic divide, demonstrating some universal scaling laws, and illustrating the vast differences in species’ ability to incorporate novel DNA and gene-expression patterns. Finally, I will review recent theory and empirical data on mutation rates across the Tree of Life, showing how random genetic drift dictates the level of refinement that can be achieved with this, and indeed any, trait.