Interactions within virtual environments often require manipulating 3D virtual objects. To this end, researchers have endeavoured to find efficient solutions using either traditional input devices or focusing on different input modalities, such as touch and mid‐air gestures. Different virtual environments and diverse input modalities present specific issues to control object position, orientation and scaling: traditional mouse input, for example, presents non‐trivial challenges because of the need to map between 2D input and 3D actions. While interactive surfaces enable more natural approaches, they still require smart mappings. Mid‐air gestures can be exploited to offer natural manipulations mimicking interactions with physical objects. However, these approaches often lack precision and control. All these issues and many others have been addressed in a large body of work. In this article, we survey the state‐of‐the‐art in 3D object manipulation, ranging from traditional desktop approaches to touch and mid‐air interfaces, to interact in diverse virtual environments. We propose a new taxonomy to better classify manipulation properties. Using our taxonomy, we discuss the techniques presented in the surveyed literature, highlighting trends, guidelines and open challenges, that can be useful both to future research and to developers of 3D user interfaces.

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