Abstract: The deployment of systems of artificial intelligence (AI) in high-risk settings warrants the need for trustworthy AI. This crucial requirement is highlighted by recent EU guidelines and regulations, but also by recommendations from OECD and UNESCO, among several other examples. One critical premise of trustworthy AI involves the necessity of finding explanations that offer reliable guarantees of soundness. This paper argues that the best known eXplainable AI (XAI) approaches fail to provide sound explanations, or that alternatively find explanations which can exhibit significant redundancy. The solution to these drawbacks are explanation approaches that offer formal guarantees of rigor. These formal explanations are not only sound but guarantee irredundancy. This paper summarizes the recent developments in the emerging discipline of formal XAI. The paper also outlines existing challenges for formal XAI.