Hydrogels are a promising material for a variety of applications after appropriate functional and structural design, which alters the physicochemical properties and cell signaling pathways of the hydrogels. Over the past few decades, considerable scientific research has made breakthroughs in a variety of applications such as pharmaceuticals, biotechnology, agriculture, biosensors, bioseparation, defense, and cosmetics. In the present review, different classifications of hydrogels and their limitations have been discussed. In addition, techniques involved in improving the physical, mechanical, and biological properties of hydrogels by admixing various organic and inorganic materials are explored. Future 3D printing technology will substantially advance the ability to pattern molecules, cells, and organs. With significant potential for producing living tissue structures or organs, hydrogels can successfully print mammalian cells and retain their functionalities. Furthermore, recent advances in functional hydrogels such as photo- and pH-responsive hydrogels and drug-delivery hydrogels are discussed in detail for biomedical applications.