Few-layer black phosphorus, a new elemental two-dimensional (2D) material recently isolated by mechanical exfoliation, is a high-mobility layered semiconductor with a direct bandgap that is predicted to strongly depend on the number of layers, from 0.35 eV (bulk) to 2.0 eV (single layer). Therefore, black phosphorus is an appealing candidate for tunable photodetection from the visible to the infrared part of the spectrum. We study the photoresponse of field-effect transistors (FETs) made of few-layer black phosphorus (3-8 nm thick), as a function of excitation wavelength, power, and frequency. In the dark state, the black phosphorus FETs can be tuned both in hole and electron doping regimes allowing for ambipolar operation. We measure mobilities in the order of 100 cm(2)/V s and a current ON/OFF ratio larger than 10(3). Upon illumination, the black phosphorus transistors show a response to excitation wavelengths from the visible region up to 940 nm and a rise time of about 1 ms, demonstrating broadband and fast detection. The responsivity reaches 4.8 mA/W, and it could be drastically enhanced by engineering a detector based on a PN junction. The ambipolar behavior coupled to the fast and broadband photodetection make few-layer black phosphorus a promising 2D material for photodetection across the visible and near-infrared part of the electromagnetic spectrum.