We discuss the relationship between invariant manifolds of
nonautonomous differential equations and pullback attractors. This
relationship is essential, e.g., for the numerical approximation
of these manifolds. In the first step, we show that the unstable
manifold is the pullback attractor of the differential equation.
The main result says that every (hyperbolic or nonhyperbolic)
invariant manifold is the pullback attractor of a related system
which we construct explicitly using spectral transformations. To
illustrate our theorem, we present an application to the Lorenz
system and approximate numerically the stable as well as the
strong stable manifold of the origin.