Quantum computers have made huge progress in recent years. In this tutorial paper, we explain why they pose a threat to encryption methods that are used in today’s communication networks. As there is the unique opportunity of 6G becoming the first cellular standard where post-quantum security could be considered from the very beginning, we present approaches to achieve post-quantum secure communications. Benefits and drawbacks of quantum key distribution (QKD) and post-quantum cryptography (PQC) are compared. Suggestions are made on how these approaches can be considered resulting in a post-quantum-safe 6G standard.