In simple terms, an asteroid retrieval mission envisages a spacecraft that rendezvous with an asteroid, lassos it and hauls it back to the Earth's neighborhood. Speculative engineering studies for such an ambitious mission concept appeared in scientific literature at the beginning of the space age. This early work employed a two-body dynamical framework to estimate the Δv costs entailed with hauling an entire asteroid back to Earth. The concept however has experienced a revival in recent years, stimulated by the inclusion of a plan to retrieve a small asteroid in NASA's 2014 budget. This later batch of work is well aware of technological limitations, and thus envisages a much more level-headed space system, capable of delivering only the most minimal change of linear momentum to the asteroid. As a consequence, the design of retrieval trajectories has evolved into strategies to take full advantage of low energy transfer opportunities, which must carefully account for the simultaneous gravitational interactions of the Sun, Earth, and Moon. The paper reviews the published literature up to date, and provides a short literature survey on the historical evolution of the concept. This literature survey is particularly focused on the design of asteroid retrieval trajectories, and thus the paper provides a comprehensive account of: the endgame strategies considered so far, the different dynamical models and the trajectory design methodologies.