We describe the magnet challenges for a Muon Collider, an exciting option considered for the future of particle physics at the energy frontier. Starting from the comprehensive work performed by the US Muon Accelerator Program, we have reviewed the performance specifications dictated by beam physics and the operating conditions to satisfy the accelerator needs. Among the many magnets that make up a muon collider, we have identified four systems that represent well the envelope of challenges: the target and capture solenoid, the final cooling solenoid, the accelerator dipoles and the collider dipoles. These systems provide focus for the development of novel concepts, largely based on HTS for reasons of performance, cost and sustainability. After giving a consolidated overview of the needs for the magnet systems, we describe here the basic technology options considered, and the plan for design and development activities.