The fundamental theory and practical procedures for estimation and inference for complex sample survey data have been under development for almost a century. The foundations are present in the work on randomization and the “representative method” (Bowley, 1906; Fisher, 1925) and what is generally agreed to be the breakthrough paper by Neyman (1934) on the theory of design-based inference from probability sample designs. Even today, estimation and inference for survey data remain an evolving field with important new developments in applications of survey data to hierarchical and latent variable modeling (Rabe-Hesketh and Skrondal, 2006), estimation of smallarea statistics (Rao, 2003), and Bayesian approaches to model estimation and inference using survey data (Little, 2003). The general concept of designbased inference and its application to survey data analysis was introduced in Section 2.2. The aim of this chapter is to expand the reader’s understanding of the key components of design-based approaches to estimation and inference from survey data: consistent estimation of population statistics; robust, distribution-free methods for estimating the sampling variance of estimates; construction and interpretation of confidence intervals; and design-adjusted test statistics for hypothesis testing.