3D bioprinting is a technology currently evolving for extensive applications within tissue engineering and regenerative medicine. The increasing demand for organ transplants and the limited supply of suitable donors have sparked significant interest in 3D bioprinting as a viable solution to organ scarcity. 3D bioprinting involves the use of a specialized biomaterial known as bioink. This medium is made up of cells embedded within a hydrogel or another type of matrix, enabling the creation of complex living tissues. Bioinks are crucial in building functional scaffolds or constructs by precisely depositing them in a pre-arranged pattern to form three-dimensional structures layer by layer. The demand for bioinks in tissue engineering, regenerative medicine, and pharmaceutical drug development is rising, leading to a steady increase in the bioink market over the next decade. In 2022, the market size is valued at 154.97 million USD, and it is projected to reach 571 million USD globally by 2029. This increasing market demand spurs the creation of different biotech companies specializing in the creation of bioinks for 3D bioprinting. This paper explores various bioink materials, including the essential properties of a bioink crucial for 3D bioprinting, as well as current market trends, commercially available bioink products, and companies considered to be key players in the bioink industry, demonstrating its potential growth and the ongoing need for innovation in bioink development to meet the expanding demands in biomedical applications. Further, this paper also discusses the manufacturing process of bioinks, which includes the three main stages of the bioprinting process, as well as the most commonly used bioprinting techniques. The review underscores the importance of advancing bioink technology to enhance the efficacy and utility of 3D bioprinted tissues and organs, enabling the creation of transplanted tissues tailored uniquely for individual patients.