Abstract Perpendicular recording has long been advocated as a means of achieving the highest areal densities. In particular, in the context of the ‘superparamagnetic limit’, perpendicular recording with a soft underlayer promises several key advantages. These advantages include a higher coercivity, thicker media that should permit smaller diameter grains and higher signal-to-noise ratio. Also, the sharper edge-writing will facilitate recording at very high track densities (lower bit aspect ratio). Recent demonstrations of the technology have shown densities comparable with the highest densities reported for longitudinal recording. This paper further examines the promise that perpendicular recording will deliver an increase in areal density two to eight times higher than that achievable with longitudinal recording. There are a number of outstanding issues but the key challenge is to create a low-noise medium with a coercivity that is high and is much larger than the remanent magnetization.