The present chapter presents two prominent and connected strands in research on puns. The first is the classification of different types according to taxonomies using a range of criteria. The second is the phonology of imperfect puns, where a punning word evokes a target that is slightly different in sound than the pun itself. It will not deal with the central phonosemantic mechanism of puns that is based on false logic (cf. Attardo, 1994, chap. 4; Hempelmann, 2003). According to this logic, described in the Platonic dialogue Kratylos (1961), the sounds of a word have a motivated relationship to the meaning of the concept that the word means. As is well known even outside linguistics and has been described succinctly by De Saussure (1983), the sounds of a linguistic sign, its signifier, have an arbitrary relationship to the meaning, the signifier. The relationship is merely a social contract adhered to by the speaker community of a language. This issue is comprehensively dealt with in another chapter of this handbook (Aarons, 2017).