The preparation of ultrahydrophobic and ultralyophobic surfaces using several techniques is described. Plasma polymerization of 2,2,3,3,4,4,4-heptafluorobutyl acrylate on poly(ethylene terephthalate) yields surfaces with water contact angles of theta(A)/theta(R) = 174 degrees/173 degrees. Argon plasma etching of polypropylene in the presence of poly(tetrafluoroethylene) renders surfaces with water contact angles as high as theta(A)/theta(R) = 172 degrees/169 degrees. Surfaces of compressed pellets of submicrometer, variable-diameter spherical particles of PTFE oligomers exhibit water contact angles of theta(A)/theta(R) = 177 degrees/177 degrees, methylene iodide contact angles of theta(A)/theta(R) = 140 degrees/138 degrees, and hexadecane contact angles of theta(A)/theta(R) = 140 degrees/125 degrees. We emphasize that contact angle hysteresis is more important in characterizing lyophobicity than is the maximum achievable contact angle. These surfaces are rough at the micrometer and submicrometer scales, and water drops roll easily on all of them. We make an intuitive argument that the topology of the roughness is important and controls the continuity of the three-phase contact line and thus the hysteresis. We also report smooth ultralyophobic surfaces that are prepared by silanization of silicon wafers with Cl(SiMe2O)(n)SiMe2Cl (n = 0, 1, 2, and 3), (Me3SiO)(n)SiCH2CH2Si(CH3)(2)Cl, and (Me3SiO)(2)Si(CH3)CH2CH2Si(CH3)(2)Cl. These surfaces exhibit much lower contact angles but little or no hysteresis, and droplets of water, hexadecane and methylene iodide slide easily off them. We propose that these covalently attached monolayers are flexible and liquidlike and that droplets in contact with them experience very low energy barriers between metastable states.