Poisson Factorization (PF) is the gold standard framework for recommendation systems with implicit feedback whose variants show state-of-the-art performance on real-world recommendation tasks. However, they do not explicitly take into account the temporal behavior of users which is essential to recommend the right item to the right user at the right time. In this paper, we introduce Recurrent Poisson Factorization (RPF) framework that generalizes the classical PF methods by utilizing a Poisson process for modeling the implicit feedback. RPF treats time as a natural constituent of the model, and takes important factors for recommendation into consideration to provide a rich family of time-sensitive factorization models. They include Hierarchical RPFthat captures the consumption heterogeneity among users and items, Dynamic RPF that handles dynamic user preferences and item specifications, Social RPF that models the social-aspect of product adoption, Item-Item RPFthat considers the inter-item correlations, and eXtended Item-Item RPF that utilizes items' metadata to better infer the correlation among engagement patterns of users with items. We also develop an efficient variational algorithm for approximate inference that scales up to massive datasets. We demonstrate RPF's superior performance over many state-of-the-art methods on synthetic dataset, and wide variety of large scale real-world datasets.