The genetic apparatus of the cell is responsible for the accurate biosynthesis of the primary structure of macromolecules which then spontaneously fold up and, in certain circumstances, aggregate to yield the complex tertiary and quaternary structures of the biologically active molecules. Structures capable of self-assembly in this range from simple monomers through oligomers to complex multimeric structures that may contain more than one type of polypeptide chain and components other than protein. It is becoming clear that even with the simpler monomeric enzymes there is becoming clear that even with the simpler monomeric enzymes there is a kinetically determined pathway for the folding process and that a folded protein must now be regarded as the minimum free energy form of the kinetically accessible conformations. It is argued that the denatured subunits of oligomeric enzymes are likely to fold to something like their final structure before aggregating to give the native quaternary structure and the available evidence would suggest that this is so. The importance of nucleation events and stable intermediates in the self-assembly of more complex structures is clear. Many self-assembling structures contain only identical subunits and symmetry arguments are very successful in accounting for the structures formed. Because proteins are themselves complex molecules and not inelastic geometric objects, the rules of strict symmetry can be bent and quasi-equivalent bonding between subunits permitted. This possibility is frequently employed in biological structures. Conversely, symmetry arguments can offer a reliable means of choosing between alternative models for a given structure. It can be seen that proteins gain stability by growing larger and it is argued in evolutionary terms that aggregation of subunits is the preferred way to increase the size of proteins. The possession of quaternary structure by enzymes allows conferral of other biologically important properties, such as cooperativity between active sites, changes of specificity, substrate channelling and sequential reactions within a multi-enzyme complex. Comparison is made of the invariant subunit compositions of the simpler oligomeric enzymes with the variation evidently open to, say, the 2-oxoacid dehydrogenase complexes of E. coli. With viruses, on the other hand, the function of the quaternary structure is to package nucleic acid and, as an example, the assembly and breakdown of tobacco mosaic virus is discussed. Attention is drawn to the possible ways in which the principles of self-assembly can be extended to make structures more complicated than those that can be formed by simple aggregation of the comonent parts.