We present the star formation history (SFH) and the age-metallicity relation (AMR) in three fields of the Fornax dwarf spheroidal galaxy. They sample a region spanning from the centre of the galaxy to beyond one core radius, which allows studying galactocentric gradients. In all the cases, we found stars as old as 12 Gyr, together with intermediate-age and young stellar populations. The last star formation events, as young as 1 Gyr old, are mainly located in the central region, which may indicate that the gas reservoir in the outer parts of the galaxy would have been exhausted earlier than in the centre or removed by tidal interactions. The AMR is smoothly increasing in the three analysed regions and similar to each other, indicating that no significant metallicity gradient is apparent within and around the core radius of Fornax. No significant traces of global UV-reionization or local SNe feedback are appreciated in the early SFH of Fornax. Our study is based on VLT photometry as deep as I ˜ 24.5 and the IAC-STAR/IAC-POP/MINNIAC suite of codes for the determination of the SFH in resolved stellar populations.