By the continuous growth of telescope size and advanced detector sensitivity the panchromatic view of galaxies is enabling us since the HST time to trace the evolution of massive galaxies observationally back to high redshifts. As examples the existence of intact gas-rich galaxy disks around redshift 2 has provided us a new insight into the gas accumulation and causes for the high star-formation rates (SFRs). Although dwarf galaxies (DGs) also exist already at that early epoch, but because of their faintness, those observations are not as feasible for them so that our wisdom of DG formation and evolution depends on assumptions from numerical simulations and from their comparison with stellar population studies of DGs in the local universe. Nevertheless, due to the improved observational facilities also for the DGs, details of their properties have affected our picture of their formation and evolution. The first impression from decades ago, that DGs possess simple structures and evolve morphologically clearly separated, has changed totally in the sense that a classical morphological division of them is meaningless in the view of the variety of DG types: there are e.g. dwarf irregular galaxies (dIrrs) with exceedingly strong star formation (SF), called starburst DGs (SBDGs), and also short but intense epochs of SF in the past, dwarf elliptical galaxies (dEs) with recent SF or central gas content, and last but not least, dwarf spheroidals (dSphs) at the faint end of dEs as satellite galaxies down to about -5m. "Normal" DGs have a brightness range between MV -18m to -10m.
For this brightness reason, dSphs are only detectible within the Local Group by refined search algorithms from surveys as e.g. SDSS. Also in the Virgo Cluster an archival work of detailed dE properties is expensive in observing time. In their studies of Virgo cluster DGs already Sandage & Biggeli  found that dEs dominate the cluster galaxy population by far, in contrast to their number fraction in the field where dIrrs are the most common DGs. This fact cannot be interpreted from the different local origins of DGs but because matter accumulates to clusters also dIrrs fall in from the cosmic web continuously whereby they have to change their morphology. Not only because of such morphological mutation but also due to the occurrence of enhanced SF in dIrrs,  emphasized already the necessity of various links between the DG types by morphological transitions.
From the CDM cosmology the baryonic matter should settle within Dark Matter (DM) halos, which originally preferred to form low-mass subhalos and hierarchically accumulate to massive galaxies. If the baryonic matter would follow this bottom-up structure formation, the subhalos should also assemble their gas at first and by this also evolve with SF to become the oldest galactic objects in the universe. That this picture seems to be too naive is simply understandable by three major physical principles:
1. The gas assembly timescale should behave as the free-fall timescale ff, namely, dependent on the gas density as g-1/2, because gas is accreted through gravitation. Whether this accretion leads to the same enhancement of SF in DGs as observed and theoretically expected  is still a matter of debate (see also sect. 2). Because the virial temperature in the DG gravitational potential does not accomplish values above 105 K, on the one hand, cold accretion  is not necessarily required as for massive halos.
2. The SF timescale SF is defined as Mg / with as the SFR that, on the other hand, in the self-regulated SF mode depends on g2 . Let me already emphasize here, that the theoretical treatment and modelling of SF self-regulation has to allow for the stellar energy of radiation and winds by massive stars already released in SF regions during their lives, i.e. prior to the explosion of supernovae typeII (SNeII). This necessity becomes clear when one continues a high SFR conditioned by gas infall and unaffected for a few million years until the first SNeII emerge. Since lower galaxy masses lead to less dense gas, SF is stretched over time for DGs.
And 3. As SF couples to stellar energy release, and since the counteracting cooling process depends on g2, the gas expands due to pressure support and reduces the SFR so that the effect of SF self-regulates non-linearly.
Another important effect that seems to affect the whole network of galaxy formation and evolution is ionizing radiation from the first cosmological objects (supermassive stars, black holes, galaxies). Due to the re-ionization of the gas in the universe, its thermodynamical state is changed so that its accretion onto low-mass objects was reduced  and gas already caught in minihalos evaporated again . Since massive objects remained almost unaffected by the re-ionization phase, while DGs should have experienced delayed SF , this evolutionary dichotomy is observed as downsizing . Nevertheless, the assumption that all DGs were affected in the re-ionization era and in the same way would request overlapping Stroemgren bubbles in an almost uniformly ionized Universe. This, however, must be questioned and is contrasted by the existence and amplification of cosmological density structures .
Another possible paths of DG origin is the formation of SF density enhancements in the tidal tails of merger galaxies . Since they should be free of DM and it is not yet well understood whether their SF acts in self-regulation the survival probability of these galaxy-like entities needs to be explored .