Catenary optics is an emerging direction of subwavelength optics, which is indispensable in describing the electric fields and dispersion property of coupled metallic subwavelength structures, and designing broadband high-efficiency geometric-phase metasurfaces. It involves catenary optical fields and catenary structures, in which both ordinary and equal-length catenary functions play important roles. In recent years, catenary optics has realized a variety of exotic phenomena and optical applications, including broadband photonic spin-Hall effect, super-resolution lithography, broadband absorbers, and extreme-angle imaging. Here, we discuss developments of catenary optics, including a brief history, physical concept and properties, applications, and future perspectives.