This chapter explores three approaches to make inference for finite populations: frequentist, Bayesian, and a novel predictive strategy enforced by martingales. The discussion commences by describing the fundamental concepts underlying sampling techniques. It subsequently differentiates between design-based and model-based inference, emphasizing the introduction of randomness through sampling designs in the former and through probabilistic models describing the random phenomenon of interest in the latter. The predictive paradigm via martingales is explored in the context of missing data, where the observed part of the population is used to construct a predictive model, which is then employed to impute the missing part of the finite population. The chapter concludes by discussing the advantages and disadvantages of each strategy.