The use of entangled light to illuminate objects is shown to provide significant enhancements over unentangled light for detecting and imaging those objects in the presence of high levels of noise and loss. Each signal sent out is entangled with an ancilla, which is retained. Detection takes place via an entangling measurement on the returning signal together with the ancilla. Quantum illumination with e bits of entanglement increases the effective signal-to-noise ratio of detection and imaging by a factor of 2^e, an exponential improvement over unentangled illumination.