How can we compute with words? Natural Language Processing is a research field focused on developing mathematical and computational models of language. For decades, models in this field were using techniques from discrete mathematics, but in recent years—with the rise of ‘deep learning’—words and sentences are increasingly modelled with continuously valued numerical vectors. Can these models deal with the endless creativity of language, where ten thousands of words can be combined into an unbounded number of potential sentences? Michael Repplinger, Lisa Beinborn, Willem Zuidema discuss the four steps the field has gone through to arrive at the current state-of-the-art vector-space models of sentences.