This paper has three purposes. The first one is to explain to a general audience what is involved in retrieving a web page or performing some other complex network transaction, and what can make it slow, and why the problem of slowness is likely to get worse as networked applications become more complex. The second is to describe, to those who program networked applications, certain facts that we have learnt from modelling communication networks, notably the fact of heavy-tailed distributions in traffic, which may allow more efficient applications to be written. The third is to describe to network modellers an interesting class of problems relating to algorithm design for communication networks.