The authors aim at creating a global picture of predictability of a dynamical system, where predictability is measured in terms of effective Lyapunov exponents. These concepts are explained in detail and it is argued that level contours of predictability are close to the stable manifolds of the most unstable set of nonwandering points. By a simple model system the authors illustrate these ideas. A detailed numerical study of a driven damped pendulum and the Lorenz model shows the utility of the predictability concept. In the former, predictability is modulated by unstable periodic orbits, in the latter by the stable manifold of a fixed point. By means of predictability, the dynamically dominant sets can be visualized. The predictability of chaotic transients for parameters of the Lorenz model where no chaotic attractor exists can be captured and predictability for values beyond the homoclinic bifurcation is given in terms of Bessel functions.