Resonant magnetic perturbations (RMP) have extensively been demonstrated as a plausible technique for mitigating or suppressing large edge localized modes (ELMs). Associated with this is a substantial amount of theory and modelling efforts during recent years. Various models describing the plasma response to the RMP fields have been proposed in the literature, and are briefly reviewed in this work. Despite their simplicity, linear response models can provide alternative criteria, than the vacuum field based criteria, for guiding the choice of the coil configurations to achieve the best control of ELMs. The role of the edge peeling response to the RMP fields is illustrated as a key indicator for the ELM mitigation in low collisionality plasmas, in various tokamak devices.