Over the last few decades, advanced manufacturing and additive printing technologies have made incredible inroads into the fields of engineering, transportation, and healthcare. Among additive manufacturing technologies, 3D printing is gradually emerging as a powerful technique owing to a combination of attractive features, such as fast prototyping, fabrication of complex designs/structures, minimization of waste generation, and easy mass customization. Of late, 4D printing has also been initiated, which is the sophisticated version of the 3D printing. It has an extra advantageous feature: retaining shape memory and being able to provide instructions to the printed parts on how to move or adapt under some environmental conditions, such as, water, wind, light, temperature, or other environmental stimuli. This advanced printing utilizes the response of smart manufactured materials, which offer the capability of changing shapes postproduction over application of any forms of energy. The potential application of 4D printing in the biomedical field is huge. Here, the technology could be applied to tissue engineering, medicine, and configuration of smart biomedical devices. Various characteristics of next generation additive printings, namely 3D and 4D printings, and their use in enhancing the manufacturing domain, their development, and some of the applications have been discussed. Special materials with piezoelectric properties and shape-changing characteristics have also been discussed in comparison with conventional material options for additive printing.