Humour has long been recognized as a key factor in enhancing creativity, group effectiveness, and employee well-being across various domains. However, its occurrence and impact within software engineering (SE) teams remains under-explored. This paper introduces a comprehensive, literature review-based taxonomy exploring the characterisation and use of humour in SE teams, with the goal of boosting productivity, improving communication, and fostering a positive work environment while emphasising the responsible use of humour to mitigate its potential negative impacts. Drawing from a wide array of studies in psychology, sociology, and organizational behaviour, our proposed framework categorizes humour into distinct theories, styles, models, and scales, offering SE professionals and researchers a structured approach to understanding humour in their work. This study also addresses the unique challenges of applying humour in SE, highlighting its potential benefits while acknowledging the need for further empirical validation in this context. Ultimately, our study aims to pave the way for more cohesive, creative, and psychologically supportive SE environments through the strategic use of humour.