Few-layer black phosphorus (BP), also known as phosphorene, is poised to be the most attractive graphene analogue owing to its high mobility approaching that of graphene, and its thickness-tunable band gap that can be as large as that of molybdenum disulfide. In essence, phosphorene represents the much sought after high-mobility, large direct band gap two-dimensional layered crystal that is ideal for optoelectronics and flexible devices. However, its instability in air is of paramount concern for practical applications. Here, we demonstrate air-stable BP devices with dielectric and hydrophobic encapsulation. Microscopy, spectroscopy, and transport techniques were employed to elucidate the aging mechanism, which can initiate from the BP surface for bare samples, or edges for samples with thin dielectric coating, highlighting the ineffectiveness of conventional scaled dielectrics. Our months-long studies indicate that a double layer capping of Al2O3 and hydrophobic fluoropolymer affords BP devices and transistors with indefinite air-stability for the first time, overcoming a critical material challenge for applied research and development.