Abstract. Highlights of studies of ULF waves from 1995 to early 1997 are presented. The subjects covered include (1) Pc 3±5 waves excited by sources in the solar wind, with emphasis on the role of the magnetospheric cavity in modifying the external source and establishing its own resonances, and the role of the plasmapause in magnetohydrodynamic wave propagation; (2) Pi 2 waves, with emphasis on the plasmaspheric resonances and possible alternative excitation by plasmasheet source waves; (3) the spatial structure of internally excited long-period waves, including a kinetic theory for radially con®ned ring current instability and groundbased multipoint observation of giant pulsations; (4) amplitude-modulated Pc 1±2 waves in the outer magnetosphere (Pc 1±2 bursts) and in the inner magnetosphere (structured Pc 1 waves or pearls); and (5) the source region of the quasi-periodic emissions. Theory and observations are compared, and controversial issues are highlighted. In addition, some future directions are suggested.