We present several questions (and some answers) about biased random walks on percolation clusters and biased random walks among random conductances. In particular,  we address ballisticity, monotonicity of the speed as a function of the strength of the bias and the Einstein relation.

The talk is based on joint works with Noam Berger, Xiaoqin Guo, Matthias Meiners, Sebastian Müller and Jan Nagel.