We introduce a novel classification framework for time-series imputation using deep learning, with a particular focus on clinical data. By identifying conceptual gaps in the literature and existing reviews, we devise a taxonomy grounded on the inductive bias of neural imputation frameworks, resulting in a classification of existing deep imputation strategies based on their suitability for specific imputation scenarios and data-specific properties. Our review further examines the existing methodologies employed to benchmark deep imputation models, evaluating their effectiveness in capturing the missingness scenarios found in clinical data and emphasising the importance of reconciling mathematical abstraction with clinical insights. Our classification aims to serve as a guide for researchers to facilitate the selection of appropriate deep learning imputation techniques tailored to their specific clinical data. Our novel perspective also highlights the significance of bridging the gap between computational methodologies and medical insights to achieve clinically sound imputation models.