The possibility for humans to interact with physical or virtual systems using gestures has been vastly explored by researchers and designers in the last 20 years to provide new and intuitive interaction modalities. Unfortunately, the literature about gestural interaction is not homogeneous, and it is characterized by a lack of shared terminology. This leads to fragmented results and makes it difficult for research activities to build on top of state-of-the-art results and approaches. The analysis in this article aims at creating a common conceptual design framework to enforce development efforts in gesture-based human-machine interaction (HMI). The main contributions of this article can be summarized as follows: 1) we provide a broad definition for the notion of functional gesture in HMI; 2) we design a flexible and expandable gesture taxonomy; and 3) we put forward a detailed problem statement for gesture-based HMI. Finally, to support our main contribution, this article presents and analyzes 83 most pertinent articles classified on the basis of our taxonomy and problem statement.