In this talk I will review some of our recent work on collaborative filtering. I will first briefly discuss probabilistic models based on matrix factorization to model changing user preferences and item popularity over time. I will also dive into some of our very recent work on inferring user exposure (to items) from click data including how we model this problem using the tools of causal inference. I will conclude by discussing some future challenges including opportunities and challenges of using these models in online environments with real-time constraints. For all projects I will report empirical and exploratory results using click data from the arXiv.org paper repository.