Due to its non-equilibrium character, active matter in a steady state can drive engines that autonomously deliver work against a constant mechanical force or torque. As a generic model for such an engine, we consider systems that contain one or several active components and a single passive one that is asymmetric in its geometrical shape or its interactions. Generally, one expects that such an asymmetry leads to a persistent, directed current in the passive component, which can be used for the extraction of work. We validate this expectation for a minimal model consisting of an active and a passive particle on a one-dimensional lattice. It leads us to identify thermodynamically consistent measures for the efficiency of the conversion of isotropic activity to directed work. For systems with continuous degrees of freedom, work cannot be extracted using a one-dimensional geometry under quite general conditions. In contrast, we put forward two-dimensional shapes of a movable passive obstacle that are best suited for the extraction of work, which we compare with analytical results for an idealised work-extraction mechanism. For a setting with many non-interacting active particles, we use a mean-field approach to calculate the power and the efficiency, which we validate by simulations. Surprisingly, this approach reveals that the interaction with the passive obstacle can mediate cooperativity between otherwise non-interacting active particles, which enhances the extracted power per active particle significantly.