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Summary form only given. Holey fibers, i.e., fibers of a new type with a cladding having a structure of a two-dimensional (often periodic) array of closely packed capillaries, allow many important problems of fiber optics to be solved and many ideas of the physics of photonic crystals to be implemented. Such fibers support single-mode waveguiding within a broad spectral range, allowing radiation energy losses to be considerably reduced in this regime. Holey fibers also hold much promise for nonlinear-optical applications. These properties of holey fibers can be employed to control the spectra of ultrashort laser pulses and to generate a supercontinuum.