Szpilrajn’s extension theorem on binary relations and its strengthening by Dushnik and Miller are fundamental in economic and game theories. Szpilrajn’s result entails that each partial order extends to a linear order. Dushnik and Miller use Szpilrajn’s theorem to show that each partial order has a realizer. Since then, many authors utilize Szpilrajn’s theorem and the well-ordering principle to prove more general theorems on extending binary relations. The original extension theorems of Szpilrajn, Dushnik-Miller and Moulin-Weymark are called: Szpilrajn extension theorem, Dushnik-Miller extension theorem and Moulin-Weymark’s Pareto extension theorem respectively. The generalizations of these theorems are called: Szpilrajn-type extension theorem, Dushnik-Miller-type extension theorem and Moulin-Weymark’s Pareto-type extension theorem respectively. The presented results generalize well-known extension theorems in the literature.