The aim of ‘programming the global computer’ was identified by Milner and others as one of the grand challenges of computing research. At the time this phrase was coined, it was natural to assume that this objective might be achieved primarily through extending programming and specification languages. The Internet, however, has brought with it a different style of computation that (although harnessing variants of traditional programming languages) operates in a style different to those with which we are familiar. The ‘computer’ on which we are running these computations is a social computer in the sense that many of the elementary functions of the computations it runs are performed by humans, and successful execution of a program often depends on properties of the human society over which the program operates. These sorts of programs are not programmed in a traditional way and may have to be understood in a way that is different from the traditional view of programming. This shift in perspective raises new challenges for the science of the Web and for computing in general.