We present some of the results obtained in collaboration with Boccardo, Leonori and Porretta about the existence of positive solutions of Dirichlet problems like $$\begin{equation} \left\{ \begin{array}{ll} -\Delta u=B\frac{|\nabla u|^2}{u}+f & \mbox{in } \Omega, \\ u=0 & \mbox{on } \partial\Omega, \end{array} \right. \end{equation}$$ where B>0 and f\ge 0 belongs to a Lebesgue space.