This chapter discusses the basics of low-order polynomial regression metamodels and their designs. This chapter is organized as follows. Section 2.1 discusses black-box versus white-box approaches in the design of simulation experiments (DASE). Section 2.2 covers the basics of linear regression analysis. Section 2.3 focuses on first-order polynomial regression. Section 2.4 presents designs for estimating such first-order polynomials; namely, so-called resolution-III (R-III) designs. Section 2.5 augments the first-order polynomial with interactions (cross-products). Section 2.6 discusses resolution-IV (R-IV) designs, which give unbiased estimators of the first-order effects—even if there are two-factor interactions. Section 2.7 presents resolution-V (R-V) designs, which also enable the estimation of all the individual two-factor interactions. Section 2.8 extends the first-order polynomials to second-order polynomials. Section 2.9 presents designs for second-degree polynomials, focussing on central composite designs (CCDs). Section 2.10 briefly examines “optimal” designs and other designs. Section 2.11 summarizes the major conclusions of this chapter. The chapter ends with appendixes, solutions for the exercises, and references.