Electroencephalogram (EEG) decoding aims to identify the perceptual, semantic, and cognitive content of neural processing based on non-invasively measured brain activity. Traditional EEG decoding methods have achieved moderate success when applied to data acquired in static, well-controlled lab environments. However, an open-world environment is a more realistic setting, where situations affecting EEG recordings can emerge unexpectedly, significantly weakening the robustness of existing methods. In recent years, deep learning (DL) has emerged as a potential solution for such problems due to its superior capacity in feature extraction. It overcomes the limitations of defining 'handcrafted' features or features extracted using shallow architectures, but typically requires large amounts of costly, expertly-labelled data -something not always obtainable. Combining DL with domain-specific knowledge may allow for development of robust approaches to decode brain activity even with small-sample data. Although various DL methods have been proposed to tackle some of the challenges in EEG decoding, a systematic tutorial overview, particularly for open-world applications, is currently lacking. This article therefore provides a comprehensive survey of DL methods for open-world EEG decoding, and identifies promising research directions to inspire future studies for EEG decoding in real-world applications.