This review is on unconventional nanolithographies that can replace the conventional photolithography. All these techniques utilize a patterned mold and the patterning is realized by physical contact of the mold with the underlying polymer layer. They are cost-effective, applicable to small feature sizes that cannot be defined by photolithography, and to an extent applicable to non-planar surfaces. Imprint and soft lithographies are reviewed first, which is then followed by new lithographies of room-temperature imprint lithography, capillary force lithography and soft molding. These new techniques are also efficient and cost-effective in fabricating complex or three-dimensional patterns and structures.