The quasi-one-dimensional electronic structure of organic charge-transfer (CT) salts rationalizes Peierls transitions in mixed or segregated stacks of pi-electron donors (D) and acceptors (A). A microscopic Peierls-Hubbard model, H-CT, is presented for CT salts with mixed stacks (D(rho+)A(rho-))(n) and ionicity rho > 0.7. Dimerization opens a Peierls gap that, due to electron correlation, is the singlet-triplet gap, EST. In contrast to spin-Peierls systems, such as Heisenberg spin chains with rho = 1 and T-SP < 20 K, Peierls transitions in CT salts with rho < 1 occur at higher T-P and involve both spin and charge degrees of freedom. Linear electron-phonon coupling and an adiabatic approximation for a harmonic lattice are used to model the dimerization amplitude delta(T) for T < T-P, the magnetic (spin) susceptibility chi(T), and the relative infrared intensity of totally symmetric molecular modes. Exact thermodynamics of HCT for stacks up to N = 12 sites are applied to two CT salts with T-P similar to 50 and 120 K whose magnetism and infrared have not been modeled previously and to CT salts with inaccessibly high T-P > 350 K whose description has been difficult. Ionic CT salts are correlated Peierls systems with a degenerate ground state (GS) at T = 0 whose elementary excitations are spin solitons, while dimerized ion-radical stacks that support triplet-spin excitons have nondegenerate GS. In less ionic CT salts, modulation of HCT parameters on cooling or under pressure leads to Peierls and/or neutral-ionic transitions of the GS, without appreciable thermal population of excited states. Correlations change the gap equation that relates EST at T = 0 to T-P compared to free electrons, and size convergence is fast in stacks with large delta(0) and high T-P.