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Agri-food systems increasingly rely on analytics, artificial intelligence, machine learning, environmental monitoring, and decision-support tools to evaluate sustainability performance. These systems can estimate resource use, model environmental impacts, detect risks, and inform actions across farms, supply chains, markets, and governance settings. As analytics become embedded in sustainability decisions, their outputs increasingly shape how environmental problems are recognised and acted upon. Yet sustainability analytics does not become useful or responsible simply because it produces indicators, predictions, rankings, or dashboards. Environmental metrics may be technically sophisticated while remaining difficult for farmers, firms, auditors, regulators, and communities to interpret or challenge. This creates an explainability problem in which users need to understand not only what an analytic system reports, but also how the result was produced, what assumptions it contains, and what consequences may follow from acting on it. This article develops a conceptual framework for explainable sustainability analytics in agri-food systems. The framework treats explainability as a system-level requirement for linking environmental impact interpretation, risk explanation, responsibility attribution, human review, and accountability safeguards. It argues that sustainability analytics should be evaluated not only by predictive performance or measurement coverage, but also by whether it supports transparent, contestable, and context-sensitive decision-making. The article contributes a structured framework for interpreting environmental impact, explaining risk, attributing responsibility, and supporting accountable review in agri-food decision contexts. It positions explainable sustainability analytics as an approach that connects data, models, indicators, explanation mechanisms, human judgement, and governance safeguards. In doing so, it provides a foundation for sustainability analytics that is more interpretable, trustworthy, and actionable.