Multilingual language models have been a crucial breakthrough as they considerably reduce the need of data for under-resourced languages. Nevertheless, the superiority of language-specific models has already been proven for languages having access to large amounts of data. In this work, we focus on Catalan with the aim to explore to what extent a medium-sized monolingual language model is competitive with state-of-the-art large multilingual models. For this, we: (1) build a clean, high-quality textual Catalan corpus (CaText), the largest to date (but only a fraction of the usual size of the previous work in monolingual language models), (2) train a Transformer-based language model for Catalan (BERTa), and (3) devise a thorough evaluation in a diversity of settings, comprising a complete array of downstream tasks, namely, Part of Speech Tagging, Named Entity Recognition and Classification, Text Classification, Question Answering, and Semantic Textual Similarity, with most of the corresponding datasets being created ex novo. The result is a new benchmark, the Catalan Language Understanding Benchmark (CLUB), which we publish as an open resource, together with the clean textual corpus, the language model, and the cleaning pipeline. Using state-of-the-art multilingual models and a monolingual model trained only on Wikipedia as baselines, we consistently observe the superiority of our model across tasks and settings.