Recently, black phosphorus (BP), an emerging layered two-dimensional (2D) material, has aroused much research interest. Distinguished from most of other 2D materials, BP is always a direct bandgap semiconductor regardless of the thickness, with the bandgap ranging from 0.3 eV (bulk) to 1.7 eV (monolayer), which is just fill the gap in the bandgap between graphene and transition metal dichalcogenides (TMDCs) in this frequency range. Besides, the BP exhibits many intriguing properties, such as high carrier mobility, highly tunable and anisotropic physical properties, which render the BP another star 2D material following graphene and TMDCs. In this review, we mainly focus on the advances in the optical properties of 2D BP, with the content covering the intrinsic optical properties and external perturbation effects on optical properties. Regarding the intrinsic optical properties, we introduce the anisotropic and layer-dependent optical absorption from interband transitions, the layer-dependent exciton binding energy and exciton absorption, visible-to-infrared photoluminescence, and stability of absorption and photoluminescence. As for external perturbation effects on optical properties, we introduce in-plane uniaxial and biaxial strain effects, gate-induced quantum confined Franz-Keldysh effect and Burstein-Moss effect. And finally we give a brief summary and outlook, pointing out some several interesting and important issues of BP, which need further studying urgently such as hyperbolic plasmons, intersubband transitions, optical properties in heterostructures and twist angle moiré superlattice and so on. This review gives an overview of the optical properties of BP and is expected to arouse the interest in further studying the BP.