The Minrank (MR) problem is a computational problem closely related to attacks on code- and multivariate-based schemes. MR can be reduced to a bilinear system of polynomial equations. In the quest to better estimate the complexity of this approach, we developed a more general theory for generic bilinear systems. In this presentation, we show some of the latest results for the complexity of MR and then, we present some general results about bilinear systems.