Machine learning methodologies can be adopted in cultural applications and propose new ways to distribute or even present the cultural content to the public. For instance, speech analytics can be adopted to automatically generate subtitles in theatrical plays, in order to (among other purposes) help people with hearing loss. Apart from a typical speech-to-text transcription with Automatic Speech Recognition (ASR), Speech Emotion Recognition (SER) can be used to automatically predict the underlying emotional content of speech dialogues in theatrical plays, and thus to provide a deeper understanding how the actors utter their lines. However, real-world datasets from theatrical plays are not available in the literature. In this work we present GreThE, the Greek Theatrical Emotion dataset, a new publicly available data collection for speech emotion recognition in Greek theatrical plays. The dataset contains utterances from various actors and plays, along with respective valence and arousal annotations. Towards this end, multiple annotators have been asked to provide their input for each speech recording and inter-annotator agreement is taken into account in the final ground truth generation. In addition, we discuss the results of some indicative experiments that have been conducted with machine and deep learning frameworks, using the dataset, along with some widely used databases in the field of speech emotion recognition.