We discuss the star formation history of the SMC region NGC 346 based on Hubble Space Telescope images. The region contains both field stars and cluster members. Using a classical synthetic CMD procedure applied to the field around NGC 346 we find that there the star formation pace has been rising from a quite low rate 13 Gyr ago to approx 1.4 times 10^{-8} Mo yr^{-1}pc^{-2} in the last 100 Myr. This value is significantly higher than in other star forming regions of the SMC. For NGC 346 itself, we compare theoretical and observed Color-Magnitude Diagrams (CMDs) of several stellar sub-clusters identified in the region, and we derive their basic evolution parameters. We find that NGC 346 experienced different star formation regimes, including a dominant and focused high density mode, with the sub-clusters hosting both pre-main sequence (PMS) and upper main sequence (UMS) stars, and a diffuse low density mode, as indicated by the presence of low-mass PMS sub-clusters. Quantitatively, the star formation in the oldest sub-clusters started about 6 Myr ago with remarkable synchronization, it continued at high rate (up to 2 times 10^{-5} Mo yr^{-1} pc^{-2}) for about 3 Myr and is now progressing at a lower rate. Interestingly, sub-clusters mainly composed by low mass PMS stars seem to experience now the first episode of star formation, following multi-seeded spatial patterns instead of resulting from a coherent trigger. Two speculative scenarios are put forth to explain the deficiency of UMS stars: the first invokes under-threshold conditions of the parent gas; the second speculates that the initial mass function (IMF) is a function of time, with the youngest sub-clusters not having had sufficient time to form more massive stars.