Black phosphorus (BP), an emerging narrow direct band-gap two-dimensional (2D) layered material that can fill the gap between the semi-metallic graphene and the wide-bandgap transition metal dichalcogenides (TMDs), had been experimentally found to exhibit the saturation of optical absorption if under strong light illumination. By taking advantage of this saturable absorption property, we could fabricate a new type of optical saturable absorber (SA) based on mechanically exfoliated BPs, and further demonstrate the applications for ultra-fast laser photonics. Based on the balanced synchronous twin-detector measurement method, we have characterized the saturable absorption property of the fabricated BPSAs at the telecommunication band. By incorporating the BP-based SAs device into the all-fiber Erbium-doped fiber laser cavities, we are able to obtain either the passive Q-switching (with maximum pulse energy of 94.3 nJ) or the passive mode-locking operation (with pulse duration down to 946 fs). Our results show that BP could also be developed as an effective SA for pulsed fiber or solid-state lasers.