This survey paper focuses on quadrotor- and multirotor- based cooperative aerial manipulation. Emphasis is first given on comparing and evaluating prototype systems that have been implemented and tested in real-time in diverse application environments. Underlying modeling and control approaches are also discussed and compared. The outcome of the survey allows for understanding the motivation and rationale to develop such systems, their applicability and implementability in diverse applications and also challenges that need to be addressed and overcome. Moreover, the survey provides a guide to develop the next generation of prototype systems based on preferred characteristics, functionality, operability and application domain.