Neural network approaches have recently shown to be effective in several information retrieval (IR) tasks. However, neural approaches often require large volumes of training data to perform effectively, which is not always available. To mitigate the shortage of labeled data, training neural IR models with weak supervision has been recently proposed and received considerable attention in the literature. In weak supervision, an existing model automatically generates labels for a large set of unlabeled data, and a machine learning model is further trained on the generated "weak" data. Surprisingly, it has been shown in prior art that the trained neural model can outperform the weak labeler by a significant margin. Although these obtained improvements have been intuitively justified in previous work, the literature still lacks theoretical justification for the observed empirical findings. In this position paper, we propose to theoretically study weak supervision, in particular for IR tasks, e.g., learning to rank. We briefly review a set of our recent theoretical findings that shed light on learning from weakly supervised data, and provide guidelines on how train learning to rank models with weak supervision.