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.