The structure of quantum interactions with fields of helicity two ("gravitons") is strongly constrained by three principles: positivity (Hilbert space), covariance, and locality of observables. To fulfil them simultaneously, one needs to work with string-localized fields. The results then follow from the condition that entities closely related to observables, like the S-matrix, be local and string-independent. They in particular reproduce the interactions dictated by general covariance in classical field theory. Graviton-matter couplings are consistent only when the graviton self-interaction is taken into account as well.