A central topic in the theory of dynamical systems is to understand the asymptotic behavior that dynamical systems can typically present. In many cases trajectories will converge to some kind of attractor, which can be a fixed point, a periodic orbit, or other type of object like a strange attractor. In this talk we will study the computability of attractors, including fixed points, periodic orbits, and some (partially) hyperbolic attractors like the Smale horseshoe or the geometrical Lorenz attractor.