This thesis groups heterogeneous results coming from three experiments. The leitmotiv is the electron behaviour in the target during and after the inter- action between a laser pulse and cold target at relativistic intensities. The measurement of the Zeeman effect in the X-ray regime by exploiting the magnetic field created by the interaction of ultra-intense fs laser pulses with solid target will be discussed in the first part. The polarization depen-dence of high resolution X-ray spectra as a tool to infer the electron velocity distribution at relativistic intensities inside the target will be matter of the second part. Finally, in the last part, the electron transport in solid plasma at intensities of about 5×1019 W/cm2 detected by an energy resolving 2D X-ray imaging system will be investigated.