The paper explores non-invertible symmetries in quantum field theory (QFT) and their implications in quantum gravity. Non-invertible symmetries generalize the product rule of groups to a more general fusion rule, and in many cases, gauged versions of these symmetries can be dual descriptions of invertible gauge symmetries. In theories with gravity, a new form of non-invertible gauge symmetry emerges in the limit of fundamental, tensionless strings. These stringy non-invertible gauge symmetries appear in standard examples such as non-abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. Both the conventional form of non-invertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate non-invertible symmetries have implications for Swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the Distance Conjecture, and can sometimes explain the existence of slightly sub-extremal states which fill in the gaps in the sublattice Weak Gravity Conjecture. The paper discusses the breaking of non-invertible symmetries by string loop effects, and illustrates this effect in examples such as non-abelian orbifolds and toroidal orbifolds. It also explores non-invertible gauge symmetries in AdS/CFT, showing that they can be realized in the bulk as stringy non-invertible gauge symmetries. The paper concludes with a discussion of the implications of these symmetries for Swampland constraints and the Weak Gravity Conjecture.The paper explores non-invertible symmetries in quantum field theory (QFT) and their implications in quantum gravity. Non-invertible symmetries generalize the product rule of groups to a more general fusion rule, and in many cases, gauged versions of these symmetries can be dual descriptions of invertible gauge symmetries. In theories with gravity, a new form of non-invertible gauge symmetry emerges in the limit of fundamental, tensionless strings. These stringy non-invertible gauge symmetries appear in standard examples such as non-abelian orbifolds. Moving away from the tensionless limit always breaks these symmetries. Both the conventional form of non-invertible gauge symmetries and these stringy generalizations are realized in AdS/CFT. Although generically broken, approximate non-invertible symmetries have implications for Swampland constraints: in certain cases they can be used to prove the existence of towers of states related to the Distance Conjecture, and can sometimes explain the existence of slightly sub-extremal states which fill in the gaps in the sublattice Weak Gravity Conjecture. The paper discusses the breaking of non-invertible symmetries by string loop effects, and illustrates this effect in examples such as non-abelian orbifolds and toroidal orbifolds. It also explores non-invertible gauge symmetries in AdS/CFT, showing that they can be realized in the bulk as stringy non-invertible gauge symmetries. The paper concludes with a discussion of the implications of these symmetries for Swampland constraints and the Weak Gravity Conjecture.