The content on the web is in a constant state of flux. New entities, issues, and ideas continuously emerge, while the semantics of the existing conversation topics gradually shift. In recent years, pretrained language models like BERT greatly improved the state-of-the-art for a large spectrum of content understanding tasks. Therefore, in this paper, we aim to study how these language models can be adapted to better handle continuously evolving web content. In our study, we first analyze the evolution of 2013 – 2019 Twitter data, and unequivocally confirm that a BERT model trained on past tweets would heavily deteriorate when directly applied to data from later years. Then, we investigate two possible sources of the deterioration: the semantic shift of existing tokens and the sub-optimal or failed understanding of new tokens. To this end, we both explore two different vocabulary composition methods, as well as propose three sampling methods which help in efficient incremental training for BERT-like models. Compared to a new model trained from scratch offline, our incremental training (a) reduces the training costs, (b) achieves better performance on evolving content, and (c) is suitable for online deployment. The superiority of our methods is validated using two downstream tasks. We demonstrate significant improvements when incrementally evolving the model from a particular base year, on the task of Country Hashtag Prediction, as well as on the OffensEval 2019 task.