The fabrication and properties of “fluoroalkylated paper” (“RF paper”) by vapor-phase silanization of paper with fluoroalkyl trichlorosilanes is reported. RF paper is both hydrophobic and oleophobic: it repels water (θappH2O>140°), organic liquids with surface tensions as low as 28 mN m-1, aqueous solutions containing ionic and non-ionic surfactants, and complex liquids such as blood (which contains salts, surfactants, and biological material such as cells, proteins, and lipids). The propensity of the paper to resist wetting by liquids with a wide range of surface tensions correlates with the length and degree of fluorination of the organosilane (with a few exceptions in the case of methyl trichlorosilane-treated paper), and with the roughness of the paper. RF paper maintains the high permeability to gases and mechanical flexibility of the untreated paper, and can be folded into functional shapes (e.g., microtiter plates and liquid-filled gas sensors). When impregnated with a perfluorinated oil, RF paper forms a “slippery” surface (paper slippery liquid-infused porous surface, or “paper SLIPS“) capable of repelling liquids with surface tensions as low as 15 mN m-1. The foldability of the paper SLIPS allows the fabrication of channels and flow switches to guide the transport of liquid droplets.