Recently, many researchers studied set containment characterizations. In this paper, we introduce some set containment characterizations for quasiconvex programming. Furthermore, we show a duality theorem for quasiconvex programming by using set containment characterizations. Notions of quasiconjugate for quasiconvex functions, especially 1, -1-quasiconjugate, 1-semiconjugate, H-quasiconjugate and R-quasiconjugate, play important roles to derive characterizations of the set containments.