We observed six fields of the Small Magellanic Cloud (SMC) with the Advanced Camera for Survey on board the Hubble Space Telescope in the F555W and F814W filters. These fields sample regions characterized by very different star and gas densities, and, possibly, by different evolutionary histories. We find that the SMC was already forming stars ~12 Gyr ago, even if the lack of a clear horizontal branch suggests that in the first few billion years the star formation activity was low. Within the uncertainties of our two-band photometry, we find evidence of a radial variation in chemical enrichment, with the SMC outskirts characterized by lower metallicity than the central zones. From our color-magnitude diagrams, we also infer that the SMC formed stars over a long interval of time until ~2-3 Gyr ago. After a period of modest activity, star formation increased again in the recent past, especially in the bar and the wing of the SMC, where we see an enhancement in the star-formation activity starting from ~500 Myr ago. The inhomogeneous distribution of stars younger than ~100 Myr indicates that recent star formation has mainly developed locally.