This article reviews soft pneumatic actuators (SPAs) that are manufactured entirely via additive manufacturing methods. These actuators are known as four-dimensional (4D)-printed SPAs and can generate bending motions in response to either pressurised or vacuum (negative pressure) air stimulus after fabrication. They are characterised by geometrical and material factors that determine their motion trajectory, and the force they exert on manipulated soft objects in delicate applications such as food handling and non-invasive surgery. Here, we review various 3D printers and materials used for the fabrication of the pressurised air bending-type SPAs. The reported approaches for modelling and control of these actuators are presented and compared. General discussions, as well as future directions and challenges of these actuators, are given.