Anisotropy refers to the property of a material exhibiting directionally dependent features. In this paper, we introduce black phosphorous (BP), the most stable allotrope of phosphorus in layered orthorhombic structure with a bandgap of 0.3 eV in bulk, as a unique 2D material in which electrons, phonons and their interactions with photons behave in a highly anisotropic manner within the plane of the layers. The unique anisotropic nature of BP thin films is revealed using angle-resolved Raman and infrared spectroscopies, together with angle-resolved transport study. For 15 nm thick BP, we measure Hall mobility of 1000 and 600 cm^2/Vs for holes along the light (x) and heavy (y) effective mass directions, respectively, at 120 K. These BP thin films also exhibit large and anisotropic in-plane optical conductivity from 2 to 5 micrometer wavelength. Field effect transistors using 4 to 30 layers of BP (2 to 15 nm) as channel material exhibit an on-off current ratio exceeding 10^5, a field-effect mobility of 205 cm^2/Vs, and good saturation properties all at room temperature, suggesting its promising future in high performance thin film electronics. By introducing narrow bandgap BP into the 2D material family, we fill the space between semi-metallic graphene and large bandgap TMDCs, where great potentials for infrared optoelectronics lie. Most importantly, the unique anisotropic nature of this intriguing material creates unprecedented possibilities for the realization of conceptually new optoelectronic and electronic devices in which angle-dependent physical properties are highly desirable.