Correlated travel-time errors bias both seismic location and location uncertainty estimates. Methodologies are introduced to model travel-time correlation structures and to account for them in standard location algorithms. A robust method based on copula theory is used for estimating variogram models for travel-time error. Generic, transportable variogram models are presented for Pn and teleseismic P phases. A linearized iterative location algorithm is introduced that takes into account the correlated travel-time error structure represented by the covariance matrix generated from the generic variogram models for a specific network. We show that ignoring the correlated error structure leads to rapidly deteriorating error ellipse coverage with increasingly correlated networks. We demonstrate through the relocation of ground truth (GT) events that taking into account the correlated model error structure significantly improves error ellipse coverage and, for unbalanced networks, reduces location bias. Monte Carlo experiments show that the deteriorating effect of non-Gaussian error distributions, albeit consistent and nonnegligible, is of secondary importance compared to the penalty paid for ignoring the correlation structure in travel-time errors.