In this paper, we prove sharp estimates and existence results for anisotropic nonlinear elliptic problems with lower order terms depending on the gradient. Our prototype is: $ \left\{ \begin{array}{ll} -\mathcal Q_{p}u =[H(Du)]^{q}+f(x) &\text{in }\Omega,\\ u=0&\text{on }\partial\Omega. \end{array} \right. $ Here $\Omega$ is a bounded open set of $\mathbb R^{N}$, $N\ge 2$, $0
