This paper compares mathematical models developed over the years to estimate the moisture content of paper after wet pressing on paper machines. Models that assume all loading pressure to act upon water are discussed in detail. In contrast, most conventional models assume that pressure splits between a hydraulic component causing water removal and a structural component supported by the fibres. This assumption is shown to be questionable in light of theoretical considerations and experimental evidence. Despite their simpler nature, models based on hydraulic forces alone are often better able to account for experimental observations. The Decreasing Permeability (DP) model is the most complete model of this form and includes all major variables affecting pressing on paper machines, thereby enabling evaluation of key factors such as the relative importance of dewatering under flow-controlled and pressure-controlled conditions together with rewetting.