The existence of starspots on late-type giant stars in close binary systems, that exhibit rapid rotation due to tidal locking, has been known for more than five decades. Photometric monitoring spanning decades has allowed studying the long-term magnetic activity in these stars revealing complicated activity cycles. The development of observing and analysis techniques that has occurred during the past two decades has also enabled us to study the detailed starspot and magnetic field configurations on these active giants. In the recent years magnetic fields have also been detected on slowly rotating giants and supergiant stars. In this paper I review what is known of the surface magnetism in the cool giant and supergiant stars.