In recent years, smart/stimuli-responsive hydrogels have drawn tremendous attention for their varied applications, mainly in the biomedical field. These hydrogels are derived from different natural and synthetic polymers but are also composite with various organic and nano-organic fillers. The basic functions of smart hydrogels rely on their ability to change behavior; functions include mechanical, swelling, shaping, hydrophilicity, and bioactivity in response to external stimuli such as temperature, pH, magnetic field, electromagnetic radiation, and biological molecules. Depending on the final applications, smart hydrogels can be processed in different geometries and modalities to meet the complicated situations in biological media, namely, injectable hydrogels (following the sol-gel transition), colloidal nano and microgels, and three dimensional (3D) printed gel constructs. In recent decades smart hydrogels have opened a new horizon for scientists to fabricate biomimetic customized biomaterials for tissue engineering, cancer therapy, wound dressing, soft robotic actuators, and controlled release of bioactive substances/drugs. Remarkably, 4D bioprinting, a newly emerged technology/concept, aims to rationally design 3D patterned biological matrices from synthesized hydrogel-based inks with the ability to change structure under stimuli. This technology has enlarged the applicability of engineered smart hydrogels and hydrogel composites in biomedical fields. This paper aims to review stimuli-responsive hydrogels according to the kinds of external changes and t recent applications in biomedical and 4D bioprinting.