The widespread proliferation of online social networks has resulted in the creation of huge amounts of data related to, among other things, the expression of opinion and sentiment about literally all aspects of everyday life. In this respect, various tools have been developed by interested parties (companies, individuals) that monitor the social media pulse with respect to various topics (products, persons, organizations, etc) in order to detect the stance, either positive or negative, and the overall emotion in the textual content of social media posts and comments. Despite the success of machine learning models for related tasks in popular languages (e.g. English), little progress has been made in under-represented languages, such as Greek. Based on this reality, in this work, we capitalize on the use of Bidirectional Encoder Representations from Transformers (BERT) architectures for emotion detection in social media textual content written in the Greek language. For this purpose, a relevant corpus is initially collected and annotated. Then, two pre-trained BERT models for the Greek language are employed, one of which has been proposed by the authors of the current work in previous publications. Both models are further trained on the collected corpus and are subsequently used in architectures that classify short social media texts in one or more emotion classes. The obtained results indicate that the BERT-based models outperform other approaches, especially those based on emotion lexicons.