The present study aims to analyse wordplay translation on the basis of the three aspects mentioned in the title — wordplay typology, translation techniques and relevant factors. The theoretical framework is eclectic but draws particularly on Delabastita (1996, 1997) and Lladó (2002). Empirical analysis is based on three English source texts and six Catalan translations, and focuses on two main issues: the frequency distribution of pairs of ST + TT segments across translation techniques, and the possible correlation(s) between translation techniques and factors influencing decision-making. It is observed that translators tend to use techniques implying a negative punning balance, i.e. resulting in some degree of loss of punning activity. Moreover, some factors identified in the literature are seen to correlate with the use of particular translation techniques. Finally, in the last section an attempt is made to go beyond description and explanation and to assess wordplay translation techniques in terms of their suitability as translation solutions.