This chapter deals with the most relevant multi-dimensional random effects panel data models, where, unlike in the case of fixed effects, the number of parameters to be estimated does not increase with the sample size. First, optimal (F)GLS estimators are presented for the textbook-style complete data case, paying special attention to asymptotics. Due to the many (semi-)asymptotic cases, special attention is given to checking under which cases the presented estimators are consistent. Interestingly, some asymptotic cases also carry a “convergence” property, that is the respective (F)GLS estimator converges to the Within estimator, carrying over some of its identification issues. The results are extended to incomplete panels and to higher dimensions as well. Lastly, mixed fixed–random effects models are visited, and some insights on testing for model specifications are considered.