  We examine critically two different recently proposed models of charge
ordering in the nominally 1/4-filled organic charge transfer solids (CTS). In
one dimension, the two models are characterized by site charge densities of the
form ...1010... and ...1100..., respectively. We establish the following
theoretical results: 1) there exists a critical nearest-neighbor Coulomb
interaction (V_c > 2|t|) only above which does the ...1010... state become the
ground state; 2) Hartree-Fock mean field theory predicts V_c incorrectly; 3)
accurate quantum Monte Carlo calculations indicate that V_c increases with
decreasing U; 4) for sufficiently strong e-ph interactions, the ...1010...
state can undergo a spin-Peierls (SP) transition; 5) for V < V_c, in the
presence of e-ph interactions, the ...1100... CO state is the ground state and
also undergoes a SP transition. We show that experimental observations clearly
indicate the ...1100... CO in the 1:2 anionic CTS and the (TMTSF)_2X class of
materials, while the results for (TMTTF)_2X with narrower one-electron
bandwidths are more ambiguous. In two dimensions, we focus on the
theta-(BEDT-TTF)_2X materials, and establish that the CO pattern there
corresponds to the so-called horizontal stripe structure, with ...1100... CO
along the two directions with larger electron hopping. We give precise
explanations of the observed spontaneous bond distortions in the c-direction of
theta-(BEDT-TTF)_2X at the metal-insulator transition and also show that the
appearance of the spin gap at lower temperatures is a true two-dimensional
effect different from the usual SP transition. Superconductivity in the charge
transfer solids appears to be limited to the class of materials which exhibits
the ...1100... CO in the insulating phase.
