The problem of sampling from a population with correlated units is considered. The presence of correlation affects all stages of a survey, from the choice of the sampling scheme to the statistical inference. Ignoring or failing to identify the existing correlation can lead to incorrect inference, such as invalid standard errors, since standard sampling techniques are no longer appropriate. In this direction, several sampling methodologies have been proposed in the literature, aiming to accommodate the correlation in both the sampling and the estimation procedure. The problem can be quite difficult when the type of correlation is completely general and existing methods rely on either restricted assumptions about the population structure or limitations to practical implementation. We provide a review of currently available methodologies, drawing attention to the properties of the derived estimates, the assumptions made, the robustness of the methods under different types of correlation and the practical limitations. A question of how these methodologies compare arises because they differ on the optimality criterion they assume towards the solution. Some methodologies are even not theoretically justified, but they are commonly used as known superior in situations of correlated measurements. The comparison study is conducted on a basis of the relative efficiencies among the competing methodologies by using simulated and real data sets.