A comprehensive overview is presented about optical fiber-based tunable photonic delay lines, which have been steadily developed over the last decade for the realization of all-optically controlled timing functions. The most widely used techniques, such as those based on slow & fast light and wavelength conversion associated to dispersion, are described and their physical limitations are discussed in terms of the maximal achievable delay, the associated signal distortion and signal bandwidth. Besides, an entirely different approach for all-optical signal delaying is introduced. This technique is based on movable grating reflectors dynamically generated in highly birefringent optical fibers. This type of delay line has experimentally demonstrated large tunable delaying with a moderate signal distortion for high capacity optical data streams and even for wideband analog signals.