Decisions made by legal adjudicators and administrative decision-makers often found upon a reservoir of stored experiences, from which is drawn a tacit body of expert knowledge. Such expertise may be implicit and opaque, even to the decision-makers themselves, and generates obstacles when implementing AI for automated decision-making tasks within the legal field, since, to the extent that AI-powered decision-making tools must found upon a stock of domain expertise, opacities may proliferate. This raises particular issues within the legal domain, which requires a high level of accountability, thus transparency. This requires enhanced explainability, which entails that a heterogeneous body of stakeholders understand the mechanism underlying the algorithm to the extent that an explanation can be furnished. However, the “black-box” nature of some AI variants, such as deep learning, remains unresolved, and many machine decisions therefore remain poorly understood. This survey paper, based upon a unique interdisciplinary collaboration between legal and AI experts, provides a review of the explainability spectrum, as informed by a systematic survey of relevant research papers, and categorises the results. The article establishes a novel taxonomy, linking the differing forms of legal inference at play within particular legal sub-domains to specific forms of algorithmic decision-making. The diverse categories demonstrate different dimensions in explainable AI (XAI) research. Thus, the survey departs from the preceding monolithic approach to legal reasoning and decision-making by incorporating heterogeneity in legal logics: a feature which requires elaboration, and should be accounted for when designing AI-driven decision-making systems for the legal field. It is thereby hoped that administrative decision-makers, court adjudicators, researchers, and practitioners can gain unique insights into explainability, and utilise the survey as the basis for further research within the field.