Despite its importance, the time variable has been largely neglected in the NLP and language model literature. In this paper, we present TimeLMs, a set of language models specialized on diachronic Twitter data. We show that a continual learning strategy contributes to enhancing Twitter-based language models′ capacity to deal with future and out-of-distribution tweets, while making them competitive with standardized and more monolithic benchmarks. We also perform a number of qualitative analyses showing how they cope with trends and peaks in activity involving specific named entities or concept drift. TimeLMs is available at github.com/cardiffnlp/timelms.