It is well known that a K3 surface is a double cover of the projective plane if and only if it has degree 2; in this case, a projective model is indeed given by a double cover of the plane ramified above a smooth sextic curve. It is then natural to move to the next step and ask when is a K3 surface a triple cover of the projective plane. In this talk, we will show that there are six possible cases, classified by the genus of their generic hyperplane section. We will provide a geometric construction of a projective model for three of them and show that one of them cannot be realized. This is joint work in progress with Francesco Polizzi.