We analyze the occurrence of knots, their spectrum, and sizes in polymer melts. Surprisingly, the number of knots in melt conformations is much lower than expected from a mapping to a random walk with the same Kuhn segment length. The effective random walk severely overrates the occurrence of knots and their complexity, particularly when compared to melts of flexible chains, indicating that nontrivial effects due to remnants of self-avoidance play a role for the chain lengths considered in this numerical study. For melt chains with higher persistence length, the effect is less pronounced. In addition, we find that chains in a melt have a knot structure very similar to dilute single chains close to the collapse transition. We finally show that typical equilibration procedures are well-suited to relax the topology in melts.