Developing rationally designed dynamic hydrogels and polymers as inks for 3D printing is in the limelight today. They would enable us to precisely fabricate complex structures in high resolutions and modular platforms with smart functions (e.g., self-healing and self-recovery), as well as tunable mechanical, chemical, and biological properties. In this paper, we explore recent developments in dynamic hydrogels and polymers as inks for 3D printing and discuss their properties and applications in tissue engineering, biomedicine, soft robotics, and sensors. The main scope of the paper is to give a deeper understanding of the field in terms of chemistry, physics, and associated properties. Moreover, the challenges and prospects of hydrogel/polymer inks will be discussed. We envisage that 3D printed dynamic hydrogels and polymers will provide unprecedented opportunities in designing and fabricating smarter structures.