Digital computers are hierarchically structured modular systems on both the hardware and software sides, embodying crucial features such as abstraction and information hiding. True complexity emerges through the interplay in this hierarchy of bottom-up and top-down effects. The latter are characterised by multiple realisability of higher level functions through lower level entities, inter alia enabling adaptive selection to generate new information from incoming data streams. Computer programs are not physical entities, but are nevertheless causally effective in numerous ways,for example facilitating causal effectiveness of social conventions such as the rules of chess and the value of money, enabling application in engineering and science of non-physical entities such as mathematical relationships and our understanding of physical laws, and facilitating social interaction through numerous applications of the internet. Their development embodies the combined experience of numerous workers in aspects ranging from basic concepts to system design to effective algorithms to high level design patterns, and is based in the extraordinary ability of digital systems to represent language, pictures,sound, mathematical relationships, and indeed all human knowledge. Hence although they are the ultimate in algorithmic causation, as characterized so precisely by Turing machines, digital computers embody and demonstrate the causal efficacy of many kinds of non-physical entities. Developing the analogies between computer systems and biological systems in terms of their structures, functioning, and development may help to understand how truly complex behaviour can emerge from simple constituents.