Deep neural networks for computer vision tasks are deployed in increasingly safety-critical and socially-impactful applications, motivating the need to close the gap in model performance under varied, naturally occurring imaging conditions. Robustness, ambiguously used in multiple contexts including adversarial machine learning, here then refers to preserving model performance under naturally-induced image corruptions or alterations. We perform a systematic review to identify, analyze, and summarize current definitions and progress towards non-adversarial robustness in deep learning for computer vision. We find that this area of research has received disproportionately little attention relative to adversarial machine learning, yet a significant robustness gap exists that often manifests in performance degradation similar in magnitude to adversarial conditions. To provide a more transparent definition of robustness across contexts, we introduce a structural causal model of the data generating process and interpret non-adversarial robustness as pertaining to a model's behavior on corrupted images which correspond to low-probability samples from the unaltered data distribution. We then identify key architecture-, data augmentation-, and optimization tactics for improving neural network robustness. This causal view of robustness reveals that common practices in the current literature, both in regards to robustness tactics and evaluations, correspond to causal concepts, such as soft interventions resulting in a counterfactually-altered distribution of imaging conditions. Through our findings and analysis, we offer perspectives on how future research may mind this evident and significant non-adversarial robustness gap.