Social media platforms host discussions about a wide variety of topics that arise everyday. Making sense of all the content and organising it into categories is an arduous task. A common way to deal with this issue is relying on topic modeling, but topics discovered using this technique are difficult to interpret and can differ from corpus to corpus. In this paper, we present a new task based on tweet topic classification and release two associated datasets. Given a wide range of topics covering the most important discussion points in social media, we provide training and testing data from recent time periods that can be used to evaluate tweet classification models. Moreover, we perform a quantitative evaluation and analysis of current general- and domain-specific language models on the task, which provide more insights on the challenges and nature of the task.