In this article I study the nature of wordplay, especially the pun, in relation to translation. The pun manipulates sounds and meanings with the intent of being witty; it takes us by surprise and evokes humour in the kick of discovery. Therefore, translating puns may be extremely difficult if the codes and cultural references differ between the two languages. The study of this problem opens with a thorough understanding of wordplay from a lexico-grammatical point of view where the pun is defined as a bisociation formed through an acoustic knot. Furthermore, the secondary, unexpected meaning of the pun takes us by surprise as it challenges so-called lexical priming in terms of the principles of collocations and colligations. Following the exposition of definitions, the chapter discusses methods and current debates on the translation of puns. The article concludes with poignant examples in the Danish translations of James Joyce’s novel Ulysses (1922), which is a playful fabric of interconnected multilingual imagery, motifs and extensive wordplay.