A temporal interface for a system component is a finite automaton that specifies the legal sequences of input events. We evaluate and compare three different algorithms for automatically extracting the temporal interface from the transition graph of a component: (1) a game algorithm that computes the interface as a representation of the most general environment strategy to avoid a safety violation; (2) a learning algorithm that repeatedly queries the component to construct the minimal interface automaton; and (3) a CEGAR algorithm that iteratively refines an abstract interface hypothesis by adding relevant state information from the component. Since algorithms (2) and (3) have been published in different software contexts, for comparison purposes, we present the three algorithms in a uniform finite-state setting. We furthermore extend the three algorithms to construct maximally permissive interface automata, which accept all legal input sequences. While the three algorithms have similar worst-case complexities, their actual running times differ greatly depending on the component whose interface is computed. On the theoretical side, we provide families of components that exhibit exponential differences in the performance of the three algorithms. On the practical side, we evaluate the three algorithms experimentally on a variety of real world examples. Not surprisingly, the experimental evaluation confirms the theoretical expectation: learning performs best if the minimal interface automaton is small; CEGAR performs best if only few component variables are needed to prove an interface hypothesis safe and permissive; and the direct (game) algorithm outperforms both approaches if neither is the case.