By comparing the results on the SFHs described in the previous section, one can infer interesting conclusions and attempt some speculations.
An interesting result of the SFH studies both in the LG and beyond is that all dwarfs have, and have had, fairly moderate SF activity. None of the dwarfs SFRs from the CMDs studied so far ever reaches values as high as 1 M / yr, and only one (NGC 1569) gets close to it [97, 98, 96]. Since 1 M / yr is the minimum rate required to let a galaxy contribute to the overabundance of faint blue objects in deep galaxy counts (see the models by ), this makes it quite unlikely that dwarfs are responsible for the blue excess.
If we look at the dwarfs shown in Fig. 20, we notice that the least active system is one of the BCDs and the most active one is the dIrr. This is not inconsistent with the findings from an extensive H study of 94 late-type galaxies , showing that the typical SFR of irregular galaxies is 10-3 M yr-1 kpc-2 and that of BCDs is generally higher. From that survey, Hunter & Elmegreen  indeed conclude that NGC 1569 and NGC 1705 are among the few systems with unusually high star formation, and that the star formation regions are not intrinsically different in the various galaxy types, except for a significantly higher spatial concentration in BCDs.
In our view, this suggests that either the morphological classification does not strictly correspond to the intensity of the SF activity, or that, most likely, the traditional classification, based in most cases on photographic plates, is rather uncertain for systems too distant to be properly resolved before the advent of HST. Probably an active dwarf such as NGC1569, hosting three Super Star Clusters and a huge number of HII regions, would have been classified as BCD, had it been just a few Mpc farther away.
If we compare the SFHs of late-type dwarfs inside and outside the LG (e.g. Fig. 15 and Fig. 20), we see that the overall scenario is quite similar, but the latter galaxies are always more active than the former at very recent epochs. Part of this is presumably due to the selection effect resulting from the difficulty of finding distant dwarf, faint galaxies, unless currently active. This effect is also the reason why early-type and quiescent dwarfs are so rare in the surveys performed so far outside the LG except for deep surveys devoted to individual galaxy clusters and groups, where they preferentially reside in central regions. Indeed, most often the HII region emission is what led to the discovery of distant dwarfs (recall that BCDs were originally called "extragalactic HII regions") and it is thus inevitable that these sytems have recent SF activity. From this point of view, it is interesting to note that the SFH of the external dwarfs of Fig. 20 is very similar in shape to that of the NGC602 region in the SMC , consistent with the circumstance that NGC602 is also associated with an HII region (N90).
How do the results on SFHs affect our understanding of galaxy formation ?
The circumstance that all dwarfs contain stars as old as the reached lookback time, independently of their metallicity, gas content or morphological classification suggests that their SF activity started at the earliest epochs. This is absolutely coherent with both the hierarchical formation scenario and the monolithical scenario. It is also consistent with downsizing if their early SFR was lower than that of more massive systems. For the (few) early-type dwarfs with studied SFH we know that this is indeed the case; how about late-type dwarfs ? We don't have direct evidences, due to the large distance of most of these systems which prevents us to reach epochs older than a few Gyrs. However, all indirect arguments go in this direction: only with quite moderate early SF activity can dIrrs and BCDs have managed to remain as metal-poor and gas-rich as they actually are. SFRs as high as the recent ones would have inevitably consumed all their gas in much less than a Hubble time and would have led to a significant chemical enrichment.
As mentioned in the Introduction, to select the most viable scenario it is the combination of the SFH with the chemical and kinematic properties of the candidate building blocks that needs to be compared with the properties of massive galaxies. In the case of local dwarfs, these properties have been recently reviewed by . Stars in classical dwarfs don't resemble those in the halo of the Milky Way, most notably their metallicity distribution functions [111, 112, 113] and the abundance ratios of elements over iron ( and references therein). Moreover, if all early-type dwarfs have had the relatively moderate SF activity shown in Fig. 17 for Cetus, with a rather long duration and the peak some Gyr after the beginning, there is no way to let them provide the iron-poor stars with high [ / Fe] typical of our halo, since the SF peak forms most of the stars when SNeIa have already had the time to pollute the medium with their iron.
On the other hand, the current knowledge of the outer Galaxy is far from complete. We know that the stellar halo hosts two distinct populations (see e.g. [114, 115] and references therein).  find that the so-called "inner halo", selected among halo stars with prograde rotation and low apogalactic maximum distance from the galactic center, is different for several aspects from the "outer halo", selected among stars with high retrograde rotation and high apogalactic maximum distance. In particular: 1) the inner halo is characterized by a tight correlation between [ / Fe] versus [Fe/H], suggesting that either the abundance ratios in distant regions of the inner halo are very similar or the inner halo developed from a well homogenized interstellar medium. In contrast, the outer halo shows a much larger scatter in [ / Fe] for a given [Fe/H], signature that the star formation was spatially inhomogeneous or these stars have been accreted from outside (from dwarf galaxies?). 2) The inner halo shows an average [ / Fe] slightly higher than observed in the outer halo, providing a clue for a more intense and short-lasting star formation activity. 3) The inner halo is only found with metallicities in the range -2.5 < [Fe/H] < -0.5, while most of the outer halo is in the range -3.5 < [Fe/H] < -1.5.
Unfortunately the outer halo is still mostly inaccessible: current high resolution abundances rely mainly on halo stars that pass near the Sun. If these stars are formed in the outer halo, their selection is biased towards higher eccentricity orbits. Avoiding this bias implies a new class of surveys able to trace variations in situ. In this context, the Gaia mission will provide a quantum leap in the ability to obtain highly precise astrometry, photometry and metallicity for a volume of several Kpc.
If the outer halo is a natural place to search for possible accretion events, the recent discovery of ultra-faint dwarfs promises to complete the picture: containing extremely metal-poor stars, probably with high [ / Fe] like in our halo [117, 118, 119], these galaxies are ideal candidates for Galactic building blocks. The problem in this case is the extreme uncertainty still affecting their measures, due to both faintness and high Galactic contamination. Overcoming these limits will be a challenge only suitable for wide-field spectrographs mounted on giant ground-based telescopes.
Over the years several interesting conversations with A. Aparicio, C. Chiosi, S. Degl'Innocenti, J. Gallagher, C. Gallart, P.G. Prada Moroni, R. Schulte-Ladbeck, S. N. Shore, E. Skillman, E. Tolstoy, and in particular L. Greggio, have been fruitful to dig into the secrets of synthetic CMD building and exploitation. We thank A. Cole for providing the Leo A figure in appropriate format and M. Monelli for the Cetus figure. We also thank Laura Greggio and the anonymous referees for detailed and constructive comments helpful to make this paper clearer. We acknowledge financial support from ASI through contract ASI-INAF I/016/07/0 and from the Italian MIUR through contract PRIN-2007JJC53X-001.