The automatic detection of implicitly offensive language is a challenge for NLP, as such language is subtle, contextual, and plausibly deniable, but it is becoming increasingly important with the wider use of large language models to generate human-quality texts. This study argues that current difficulties in detecting implicit offence are exacerbated by multiple factors: (a) inadequate definitions of implicit and explicit offense; (b) an insufficient typology of implicit offence; and (c) a dearth of detailed analysis of implicitly offensive linguistic data. (...) In this study, based on a qualitative analysis of an implicitly offensive dataset, a new typology of implicitly offensive language is proposed along with a detailed, example-led account of the new typology, an operational definition of implicitly offensive language, and a thorough analysis of the role of figurative language and humour in each type. Our analyses identify three main issues with previous datasets and typologies used in NLP approaches: (a) conflating content and form in the annotation; (b) treating figurativeness, particularly metaphor, as the main device of implicitness, while ignoring its equally important role in the explicit offence; and (c) an over-focus on form-specific datasets (e.g. focusing only on offensive comparisons), which fails to reflect the full complexity of offensive language use. (shrink)