A series of ab initio simulations, based on density functional theory, of the structure of the clean GaAs-(001)-(2 × 4) surface and of C 2 H 2 , C 2 H 4 , and trimethylgallium (TMGa) adsorbates are described. This surface was selected because of its importance in the growth of GaAs by molecular beam epitaxy. After summarizing briefly the theoretical basis of the computational methods used in the paper, we review critically what is known from experiment and theory about the structure of the clean surface. We argue that there is now strong evidence in favor of the "trench dimer" model for the -phase of the clean surface, while the structures of the R and γ phases are less settled. We then present ab initio simulations of the trench dimer, the three dimer, and the gallium rebonded models of the clean GaAs(001)-(2 × 4) surface and discuss their common structural and bonding features. Ab initio simulations of C 2 H 2 and C 2 H 4 adsorbates at arsenic dimers of the GaAs(001)-(2 × 4) surface are then presented. The changes in the bonding configurations of both the adsorbates and the surface arsenic dimers are explained in terms of changes in the bond orders and local hybridization states. The As dimer bond is broken in the stable chemisorbed states of the molecules. However, an intermediate state, in which the As dimer is still intact, provides a significant barrier to chemisorption in both cases. This barrier, and its absence at the Si(001) surface, stems from the two extra electrons in the As dimer compared with the Si dimer. We then go on to describe the results of 14 ab initio simulations of structures connected with the chemisorption and decomposition of TMGa on the GaAs(001)-(2 × 4) surface. TMGa is commonly used in the growth of GaAs crystals from the vapor phase. The results of these simulations are used to explain a number of experimental observations concerning the surface coverage and the decomposition of TMGa to dimethylgallium and monomethylgallium. Significant technical aspects of the calculations, notably the number of relaxed layers in the slab calculations and the necessity to use gradient-corrected adsorption energies, are stressed. The paper also contains critical comments about ab initio simulations of the GaAs-(001)-(2 × 4) clean surface and about the model based on a "linear combination of structural motifs".