The outranking approach and the foundations of ELECTRE methods were introduced by Bernard Roy of LAMSADE, Université de Paris-Dauphine. The concept of outranking relations emerged from challenges in solving various real-world problems. Since its inception, the concept has been applied in numerous fields, with recent examples including works by Barda et al., Clímaco et al., Martel and Nadeau, Maystre and Simos, Parent and Schnabele, Rabeharisoa, Renard, Roy et al., Slowinski and Treichel. Many more applications can be found in other works by Jacquet-Lagrèze and Siskos, de Montgolfier and Bertier, Roy, and Schärlig. The first part of the paper describes the main features of real-world problems suitable for the outranking approach and introduces the concept of outranking relations. The second part discusses the basic ideas and concepts used to build outranking relations. Part three defines these relations for the main ELECTRE methods. The final part addresses practical considerations. In the introduction, preliminary notations and definitions are provided. A set A of potential actions (alternatives) is considered, which may not be exclusive. A consistent family F of n criteria g_j is defined, reflecting the preferences of decision-makers. The performance of an action a under criterion j is denoted g_j(a). It is assumed that g_j(a) is a real number, even if it represents a qualitative assessment. For a given criterion k, imprecision or uncertainty in performance evaluation may lead an actor to judge an action a' as indifferent to a, even if g_k(a') ≠ g_k(a), or strictly preferred to a if the difference g_k(a') - g_k(a) is sufficiently significant.The outranking approach and the foundations of ELECTRE methods were introduced by Bernard Roy of LAMSADE, Université de Paris-Dauphine. The concept of outranking relations emerged from challenges in solving various real-world problems. Since its inception, the concept has been applied in numerous fields, with recent examples including works by Barda et al., Clímaco et al., Martel and Nadeau, Maystre and Simos, Parent and Schnabele, Rabeharisoa, Renard, Roy et al., Slowinski and Treichel. Many more applications can be found in other works by Jacquet-Lagrèze and Siskos, de Montgolfier and Bertier, Roy, and Schärlig. The first part of the paper describes the main features of real-world problems suitable for the outranking approach and introduces the concept of outranking relations. The second part discusses the basic ideas and concepts used to build outranking relations. Part three defines these relations for the main ELECTRE methods. The final part addresses practical considerations. In the introduction, preliminary notations and definitions are provided. A set A of potential actions (alternatives) is considered, which may not be exclusive. A consistent family F of n criteria g_j is defined, reflecting the preferences of decision-makers. The performance of an action a under criterion j is denoted g_j(a). It is assumed that g_j(a) is a real number, even if it represents a qualitative assessment. For a given criterion k, imprecision or uncertainty in performance evaluation may lead an actor to judge an action a' as indifferent to a, even if g_k(a') ≠ g_k(a), or strictly preferred to a if the difference g_k(a') - g_k(a) is sufficiently significant.