The chemisorption of oxygen on the Ru(001) surface shows ordered p(2×2) and p(1×2) phases at coverages of 1/4 and 1/2 monolayer, respectively, that are observed to undergo apparently continuous transitions to a disordered state upon heating. We present here details of the experimental determination of the O/Ru phase diagram, lattice-gas models that describe it, and some (but not all) of the observed critical behavior. Monte Carlo simulations based on a phenomenological Hamiltonian describing pairwise interactions between adatoms are used to calculate the phase boundaries and (effective) critical exponents. Restricting adsorption of oxygen atoms to the triangular lattice of the hcp-type hollow sites as seen experimentally, repulsive first- and second-nearest-neighbor interactions are sufficient to describe the observed phase diagram at coverages Θ<0.4 and the four-state Pott’s-class critical exponents at Θ=1/4, but fail to describe the higher coverage region. This model is then generalized to allow oxygen adsorption on both hcp- and fcc-type hollow sites, with a difference in binding energy of 0.52 eV between the two types of sites. At higher coverages, repulsive interactions within the adsorbate lead to a spillover of up to 12% of adatoms onto the sites of higher energy, markedly reducing the transition temperature at Θ=1/2, in agreement with the experimental results on O/Ru(001). However, effective critical exponents computed for this model are near four-state Pott’s values at Θ=1/2, in contrast to the experimental data and suggestive of crossover behavior involving (2×2)-honeycomb and p(2×1) ground states.