The present paper comprises direct numerical simulation of the mixing of passive and reactive scalars in two-dimensional flows dominated by coherent vortices. By means of highly accurate pseudo-spectral methods the instationary Navier-Stokes and convection-diffusion-reaction equations are numerically integrated on the torus. We present the evolution of typical vortex arrangements and analyze their ability to mix scalars. Furthermore, we attribute the influence of vortices on the mixing to the formation of spirals and to the merging of vortices. As a way of quantifying the mixing, we consider global and local mixing time scales which describe the overall and the early variance decay, respectively. Moreover, the influence of the Schmidt number and of a chemical reaction on mixing processes are investigated.