K-essence models – scalar field theories with non-quadratic kinetic terms – are considered candidates for dynamical dark energy and inflation. One of the most interesting features of these nonlinear theories is that perturbations around nontrivial backgrounds propagate with a speed different from the speed of light. In particular, superluminal propagation is possible. In my talk, I will review the k-essence paradigm emphasizing the issues related to causality. I will show that superluminal propagation does not lead to any additional causal paradoxes over and above those already present in standard general relativity. I will end by presenting a model which allows the obtaining of information from beyond the horizon of a black hole.