This paper introduces reviewability as a framework for improving the accountability of automated and algorithmic decisionmaking (ADM) involving machine learning. We draw on an understanding of ADM as a socio-technical process involving both human and technical elements, beginning before a decision is made and extending beyond the decision itself. While explanations and other model-centric mechanisms may assist some accountability concerns, they often provide insufficient information of these broader ADM processes for regulatory oversight and assessments of legal compliance. Reviewability involves breaking down the ADM process into technical and organisational elements to provide a systematic framework for determining the contextually appropriate record-keeping mechanisms to facilitate meaningful review - both of individual decisions and of the process as a whole. We argue that a reviewability framework, drawing on administrative law's approach to reviewing human decision-making, offers a practical way forward towards more a more holistic and legally-relevant form of accountability for ADM.