It is common practice in high-dimensional data analysis that a model selection is first performed and then inference is carried out using the selected model presuming that the chosen model is the true model; that is, without accounting for model selection uncertainty. Recently, methods such as clean and screen are being used to account for model selection uncertainty. However, the robustness and the efficiency properties of the resulting statistical procedures are largely unknown. In this presentation, we provide a systematic account of efficiency and robustness properties of post-selection estimators. In the process we address some foundational questions concerning the role of moderate deviation theory in the study of statistical efficiency and robustness and their trade-offs.