The spectrum of intense femtosecond optical pulses after propagation through transparent nonlinear medium contains precious information on the phase and amplitude of the optical pulse, provided the nonlinear response of the medium is known. Alternatively, knowing the phase and amplitude of the optical pulse, it is possible to extract with high accuracy the nonlinear Ken response of the medium. Examples of pulse characterisation and determination of Ken coefficients of different solids, liquids, and gases will be presented. A particular interesting phenomenon occurs in air, where spontaneous revivals of the nonlinearity are observed well after the passage of the pulse.