Few-layer black phosphorus, a new elemental 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 nm to 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 current ON/OFF ratio larger than 10 3 . Upon illumination, the black phosphorus transistors show response to excitation wavelengths from the visible up to 940 nm and 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