Low luminosity (dwarf) galaxies play a crucial role in our current theories of galaxy and large scale structure formation. In the hierarchical picture they are the building blocks from which other structures form. These theories in their basic form overpredict the numbers of small dark matter halos (dwarf galaxies?) unless some form of star formation supression is invoked. In this paper we describe observations of dwarf galaxies in a range of different environments. We find that there are far too few dwarf galaxies in low density environments to be compatible with the theories. These observations are not consistent with an environment-independent mechanism suppressing dwarf galaxy formation. It is also not clear how these mechanisms can supress star formation if dwarf galaxies have large mass-to-light ratios (≈100). Either the whole idea of hierarchical galaxy formation has to be rejected or other environmentally dependent physical processes have to be invoked. We suggest that small, gas-rich dI galaxies have their evolution rapidly advanced as they move into the dense cluster environment.