This paper aims to establish six-dimensional (6D) printing as a new branch of additive manufacturing investigating its benefits, advantages as well as possible limitations concerning the design and manufacturing of effective smart structures. The concept of 6D printing, to the authors’ best knowledge, is introduced for the first time. The new method combines the four-dimensional (4D) and five-dimensional (5D) printing techniques. This means that the printing process is going to use five degrees of freedom for creating the final object while the final produced material component will be a smart/intelligent one (i.e., will be capable of changing its shape or properties due to its interaction with an environmental stimulus). A 6D printed structure can be stronger and more effective than a corresponding 4D printed structure, can be manufactured using less material, can perform movements by being exposed to an external stimulus through an interaction mechanism, and it may learn how to reconfigure itself suitably, based on predictions via mathematical modeling and simulations.