Absorbent foam materials that are capable of acquiring and distributing aqueous fluids, especially discharged body fluids such as urine. These absorbent foams combine relatively high capillary absorption pressures and capacity-per-weight properties that allow them to acquire fluid, with or without the aid of gravity. These absorbent foams also give up this fluid efficiently to higher absorption pressure storage materials, including foam-based absorbent fluid storage components, without collapsing. These absorbent foams are made by polymerizing high internal phase emulsions (HIPEs).