This paper presents EstBERT, a large pretrained transformer-based language-specific BERT model for Estonian. Recent work has evaluated multilingual BERT models on Estonian tasks and found them to outperform the baselines. Still, based on existing studies on other languages, a language-specific BERT model is expected to improve over the multilingual ones. We first describe the EstBERT pretraining process and then present the models' results based on the finetuned EstBERT for multiple NLP tasks, including POS and morphological tagging, dependency parsing, named entity recognition and text classification. The evaluation results show that the models based on EstBERT outperform multilingual BERT models on five tasks out of seven, providing further evidence towards a view that training language-specific BERT models are still useful, even when multilingual models are available.