Many modern high-performing machine learning models increasingly rely on scaling up models, e.g., transformer networks. Simultaneously, a parallel line of work aims to improve the model performance by augmenting an input instance with other (labeled) instances during inference. Examples of such augmentations include task-specific prompts and similar examples retrieved from the training data by a nonparametric component. Despite a growing literature showcasing the promise of these retrieval-based models, their theoretical underpinnings %for such models remain under-explored. In this paper, we present a formal treatment of retrieval-based models to characterize their performance via a novel statistical perspective. In particular, we study two broad classes of retrieval-based classification approaches: First, we analyze a local learning framework that employs an explicit local empirical risk minimization based on retrieved examples for each input instance. Interestingly, we show that breaking down the underlying learning task into local sub-tasks enables the model to employ a low complexity parametric component to ensure good overall performance. The second class of retrieval-based approaches we explore learns a global model using kernel methods to directly map an input instance and retrieved examples to a prediction, without explicitly solving a local learning task.