The inert doublet model is a minimal extension of the Standard Model which accounts for the dark matter of the Universe and which consists in introducing one extra scalar field, odd under an unbroken Z2 symmetry, with identical gauge quantum number as the Standard Model Higgs. We discuss in this talk the signatures of this model, with emphasis on the indirect dark matter detection. In particular, we show that the model predicts the existence of sharp features in the gamma-ray spectrum that might be at the reach of future gamma-ray telescopes.