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We review the theoretical limits which restrict transmission over optical fibers. The fundamental limit on channel capacity is 1 nat/photon with a coherent detection receiver or with a thermal-noise-limited receiver. With an ideal photon-counting receiver, the theoretical capacity is infinite. A practical limit of a few nats per photon for direct detection requires a bandwidth expansion consistent with monomode fibers and fast digital circuits and is 35-40 dB better than current direct detection receivers. This limit may be approached by receiver improvements (10 dB with direct detection, 17 dB with optimum coherent detection), by using digital pulse-position modulation (PPM) (10-13 dB) and by using error-correcting codes where constraints on system complexity allow.