When multiple victim species (e.g. prey, host) are attacked by one or more shared enemy species (e.g. predator, pathogen), the potential exists for apparent competition between victim populations. We review ideas on apparent competition (also called ''competition for enemy-free space'') and sketch illustrative examples. One puzzling aspect of this indirect interaction is the repeated rediscovery of the essential ideas. Apparent competition arises between focal and alternative prey populations because, in the long term, enemy abundance depends on total prey availability; by increasing enemy numbers, alternative prey intensify predation on focal prey. A frequent empirical finding, consistent with theory, is exclusion of victim species from local communities by resident enemies. Theory suggests victim-species coexistence depends on particular conditions. To understand fully the consequences of shared enemies requires a body of contingent theory, specifying the time-scale of the interactions (short-and long-term consequences of sharing enemies generally differ), the structure of the food-web encompassing the interactions, its spatial context, etc. The ''core criterion'' for a focal victim species to invade a community supporting a resident, polyphagous enemy is r > aP (the invader's intrinsic rate of increase should exceed attack rate times average enemy abundance). A growing body of data and observations test, and support, this prediction.