The evolution of computing is an example of a major, transformative technological adaptation still unfolding in human history. Information technologies are supported by many other knowledge domains that have evolved through a cumulative cultural process, yet at the same time computing affects the tempo and mode of cultural evolution, greatly accelerating innovation processes driven by recombination of present technologies. Additionally, computing has created entire new domains for cumulative cultural evolution, furthering an era dominated by digital economies and media. These new domains offer very desirable qualities for cultural evolution research and digital archaeology, including good coverage in data completeness in widely different aspects of human culture, from social networks to innovation in programming languages. We review the major transitions in information technologies, with especial interest in their connections to a biological evolutionary framework. In particular, software vs. hardware evolution poses an interesting example of symbiotic technologies that display strong social dependencies as well as an extrinsic fitness due to energetic and temporal constrains. Properly accounting for the interplay of material and social factors can explain the coexistence of gradualism and punctuated dynamics in cultural and technological evolution.