We focus on the problem of selecting meaningful tweets given a user's interests; the dynamic nature of user interests, the sheer volume, and the sparseness of individual messages make this a challenging problem. Specifically, we consider the task of time-aware tweets summarization, based on a user's history and collaborative social influences from "social circles." We propose a time-aware user behavior model, the Tweet Propagation Model (TPM), in which we infer dynamic probabilistic distributions over interests and topics. We then explicitly consider novelty, coverage, and diversity to arrive at an iterative optimization algorithm for selecting tweets. Experimental results validate the effectiveness of our personalized time-aware tweets summarization method based on TPM.