When a powerful femtosecond laser pulse propagates in an optical medium, self-focusing occurs. Normally, it is the most powerful part (slice) of the pulse that self-focuses first during its propagation. Self-focusing is balanced by the creation of plasma in the self-focal volume, which defocuses the pulse. This balance leads to a limitation of the peak intensity (intensity clamping). The series of self-foci from different slices of the front part of the pulse give rise to the perception of a so-called filament. The back part of the pulse undergoes self-phase modulation and self-steepening resulting in a strong spectral broadening. The final pulse is a white-light laser pulse (supercontinuum). The physics of such (long distance) filamentation and the self-transformation process are reviewed both in air and in condensed matters. The self-transformation leads to a shorter pulse and is currently being studied for efficient pulse compression to the single and (or) few-cycle level. The efficient generation of a third harmonic in the filament is due to a new phenomenon called self-phase locking. The potential applications in atmospheric sensing and lightning control will be briefly discussed. The capability of melting glass leading to index change will be underlined. The paper will end with an outlook into the future of the field. PACS Nos.: 42.65, 42.65Jx, 42.25, 42.79Qx

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