In cognitive decoding, researchers aim to characterize a brain region's representations by identifying the cognitive states (e.g., accepting/rejecting a gamble) that can be identified from the region's activity. Deep learning (DL) methods are highly promising for cognitive decoding, with their unmatched ability to learn versatile representations of complex data. Yet, their widespread application in cognitive decoding is hindered by their general lack of interpretability as well as difficulties in applying them to small datasets and in ensuring their reproducibility and robustness. We propose to approach these challenges by leveraging recent advances in explainable artificial intelligence and transfer learning, while also providing specific recommendations on how to improve the reproducibility and robustness of DL modeling results.