Side-channel attacks represent a realistic and serious threat to the security of embedded devices for already almost three decades. A variety of attacks and targets they can be applied to have been introduced, and while the area of side-channel attacks and their mitigation is very well-researched, it is yet to be consolidated. Deep learning-based side-channel attacks entered the field in recent years with the promise of more competitive performance and enlarged attackers’ capabilities compared to other techniques. At the same time, the new attacks bring new challenges and complexities to the domain, making the systematization of knowledge (SoK) even more critical. We first dissect deep learning-based side-channel attacks according to the different phases they can be used in and map those phases to the efforts conducted so far in the domain. For each phase, we identify the weaknesses and challenges that triggered the known open problems. We also connect the attacks to the threat models and evaluate their advantages and drawbacks. Finally, we provide a number of recommendations to be followed in deep learning-based side-channel attacks.