In this paper we introduce a definition of post-Turing ICT with an initial analysis of its sustainability. At the beginning of the history of computing the attention was concentrated on the single machine: a device able to read and write a memory and able to execute different actions depending on the internal state. It was only in the 1960’s that the fifth function (after input, memory, processing and output) was introduced: the network, the capability of this single computational node to be connected and exchange data with similar machines. In the last fifty years the network has grown at an incredible speed, introducing us into the post-Turing ICT era: billions of electronic devices interconnected. ICT has now a significant environmental impact along all its lifetime phases: manufacturing (based on scarce minerals), application (based on growing power consumption) and e-waste management (with open cycles difficult to close). In this paper, we introduce relevant topics to understand whether the current ICT production and consumption paradigms are sustainable, and the social consequences and implications of such a problem for stakeholders.