Approximate Bayesian computation (ABC) is becoming an accepted tool for statistical analysis in models with intractable likelihoods. With the initial focus being primarily on the practical import of ABC, exploration of its formal statistical properties has begun to attract more attention. In this talk we consider the asymptotic behavior of the posterior distribution obtained from ABC and the ensuing posterior mean, as well as the asymptotic behaviour of tests based on ABC distributions. These results hold under given rates for the tolerance used within ABC, mild regularity conditions on the summary statistics, and a condition linked to identification of the true parameters. Using simple illustrative examples that have featured in the literature, we demonstrate that the required identification condition is far from guaranteed. The implications of the theoretical results for practitioners of ABC are also highlighted. We further detail the robustness of various ABC procedures under model misspecification.