In this talk we investigate the problem of computing the domain of attraction of a continuous-time flow on $\mathbb{R}^2$ for a given attractor. We consider an operator that takes two inputs, the description of the flow and a cover of the attractor, and that outputs the domain of attraction for the given attractor. We show that: (i) if we consider only (structurally) stable systems, the operator is computable; (ii) if we allow all systems defined by $C^1$-functions, the operator is not computable. We also address the problem of computing limit cycles on these systems.