Filtration media including at least one layer of nanofibers having average diameters less than 1000 nanometers with optional scrim layer(s) are disclosed for filtering particulate matter in liquid. The media achieve flow rates of at least 0.055 L/min/cm.sup.2 at relatively high levels of solidity. The media have also advantageously been found to have non-diminishing flow rates as differential pressures increase between 2 psi (14 kPa) and 15 psi (100 kPa).