Much information from condensed matter systems is obtained by scattering experiments such as neutron scattering or ARPES. Through linear response theory, the observed quantities relate to the dynamical correlation functions of the system at hand. While it is easy to write down a formal expression for these, it is in general a very hard problem to obtain numerically or analytically any physically meaningful result for strongly interacting systems. In this talk I will review some of the progress in understanding these dynamical correlations in one-dimensional systems based on bosonization, nonlinear Luttinger liquid theory and integrable models. I will touch on experiments on quantum wires as a motivation and illustrate the techniques with results on certain model systems.