The principal challenges arising from beam-induced energy deposition in superconducting (SC) magnets at high-energy high-luminosity hadron and lepton colliders are described. Radiation constraints are analyzed that include quench stability, dynamic heat loads on the cryogenic system, radiation damage limiting the component lifetime, and residual dose rates related to hands-on maintenance. These issues are especially challenging for the interaction regions (IR), particularly for the considered upgrade layouts of the Large Hadron Collider. Up to a few kW of beam power can dissipate in a single SC magnet, and a local peak power density can substantially exceed the quench levels. Just formally, the magnet lifetime is limited to a few months under these conditions. Possible solutions and the ways to mitigate these problems are described in this paper along with R&D needed
