Homological projective duality(HPD) was introduced in 2005 by A. Kuznetsov. The construction gives a powerful method of producing semiorthogonal decompositions of the derived category of coherent sheaves on algebraic varieties. More precisely it allows to describe the derived categories of all complete linear sections of an algebraic variety. Among the interesting examples where HPD is well understood are the projective space in the double Veronese embedding and Gr(2,n) (for n lower or equal to 7) with the Plucker embedding. In this talk I will try explain the general context of HPD and then describe some results regarding Gr(3,6).