Objective. When a person listens to continuous speech, a corresponding response is elicited in the brain and can be recorded using electroencephalography (EEG). Linear models are presently used to relate the EEG recording to the corresponding speech signal. The ability of linear models to find a mapping between these two signals is used as a measure of neural tracking of speech. Such models are limited as they assume linearity in the EEG-speech relationship, which omits the nonlinear dynamics of the brain. As an alternative, deep learning models have recently been used to relate EEG to continuous speech. Approach. This paper reviews and comments on deep-learning-based studies that relate EEG to continuous speech in single- or multiple-speakers paradigms. We point out recurrent methodological pitfalls and the need for a standard benchmark of model analysis. Main results. We gathered 29 studies. The main methodological issues we found are biased cross-validations, data leakage leading to over-fitted models, or disproportionate data size compared to the model's complexity. In addition, we address requirements for a standard benchmark model analysis, such as public datasets, common evaluation metrics, and good practices for the match-mismatch task. Significance. We present a review paper summarizing the main deep-learning-based studies that relate EEG to speech while addressing methodological pitfalls and important considerations for this newly expanding field. Our study is particularly relevant given the growing application of deep learning in EEG-speech decoding.