This paper reviews the effect of multirotor aerial vehicle designs on their abilities in terms of tasks and system properties. We propose a general taxonomy to characterize and describe multirotor aerial vehicles and their designs, which we apply exhaustively on the vast literature available. Thanks to the systematic characterization of the designs, we exhibit groups of designs having the same abilities in terms of achievable tasks and system properties. In particular, we organize the literature review based on the number of atomic actuation units and we discuss global properties arising from their choice and spatial distribution in the mechanical designs. Finally, we provide a discussion on the common traits of the designs found in the literature and the main open and future problems.