The physical quantity describing atmospheric effect on vision is visibility. The definitions of visibility have been diverse in different application areas and scientific literatures. Horizontal visibility was measured routinely in meteorology. There has been no standard visibility definition for slant path vision which is frequently occurred in such areas as aeronautics. Based on the radiance contract between object and atmospheric background the problem on vision through atmosphere is discussed. Definition of horizontal visibility has been clarified. The slant path visibility has been solved based on the radiative transfer equation. The general characteristics of the slant path visibility under model atmosphere are presented, and emphasis is paid on the difference between up-looking and down-looking visibility.