Robots play an important role all over the world in the industrial field in terms of dealing with various materials, performing duties quickly and high accuracy as well as in the pharmaceutical/chemical field since robots can handle some issues better than human. Robotic manipulation is the term used to describe how robots deal with many objects. This article reviews the contact and non-contact manipulation with their most common robotic applications and focusing on the non-contact manipulation since it can do specific tasks which contact manipulation cannot do. Reviewing of the robotic non-contact manipulation which include the metal-based robotic manipulation such as magnetic and electrostatic levitation and the non-metal-based robotic manipulation method such as aerodynamic and acoustic levitation have been made in this article. The main core of this article is acoustic levitation which considered one of the most important levitation and manipulation method due to the recent advancements that made it proper to deal with any kind of materials. Here, we review the renowned three methods of acoustic levitation that already using in robotic non-contact manipulation which are standing wave, near-field and single-beam acoustic levitation. Then, we present a performance characteristic of the reviewed methods and the summary of controlling strategies, followed by conclusion and future recommendations for acoustic levitation methods as a non-contact manipulation.