Kinematic singularity- and zero-free invariant amplitudes for Compton scattering of spin-one particles are derived. Gauge invariance is automatically satisfied. A complete set of low-energy theorems is obtained. In addition to the well-known first-order theorems, higher-order theorems also exist. It is shown that up to second order in the photon energy the 12 independent amplitudes are determined by the static moments of the target particle plus four dynamic structure-dependent constants; up to third order they are determined by the static moments plus eight additional constants. Dispersion relations may be written down for the invariant amplitudes without any ad hoc subtractions. The asymptotic behavior of these amplitudes is carefully examined, leading to a systematic derivation of possible sum rules and superconvergence relations. Generalizations of previously known sum rules as well as new ones are obtained.