Explainable artificial intelligence (XAI) is a new recent area that encompasses techniques attempting to better explain to humans how a given trained machine learning (ML) model work ensuring they can trust, understand and appropriately manage the model. On the other hand, multi-objective optimization (MOO) includes a series of algorithms that attempt to minimize or maximize, at the same time, two or more discordant objectives. One of XAI’s current challenges is balancing accuracy and human interpretability – a tradeoff of two conflicting goals. Therefore, the adoption of MOO techniques within XAI might be suitable. Surprisingly, there is a minimal amount of literature available addressing both areas. This document proposes a systematic literature review to identify the primary research in both fields.