Interactivity is an important feature of data analysis, as the choice of questions asked about a dataset often depends on previous interactions with the same dataset.  Interaction invalidates most statistical methods for preventing overfitting and ensuring generalization.  In this talk I will give an introduction to a recent line of work that aims to understand when and how it is possible to ensure generalization in interactive data analysis.  The main theme of this work is that strong notions of algorithmic stability ensure generalization, even in interactive settings.