The Singlet-Doublet model of dark matter is a minimal extension of the Standard Model with dark matter that is a mixture of a singlet and a non-chiral pair of electroweak doublet fermions. The stability of dark matter is ensured by the typical parity symmetry, and, similar to a "Bino-Higgsino" system, the extra matter content improves gauge coupling unification... We revisit the experimental constraints on the Singlet-Doublet dark matter model, combining the most relevant bounds from direct (spin independent and spin dependent) and indirect searches. We show that such comprehensive analysis sets strong constraints on a large part of the 4-dimensional parameter space, closing the notorious "blind-spots" of spin independent direct searches. Our results emphasise the complementarity of direct and indirect searches in probing dark matter models in diverse mass scale regimes. We also discuss the LHC bounds on such scenario, which play a relevant role in the low mass region of the dark matter candidate. (read more)