Over the years, 3D printing technologies have transformed the field of tissue engineering and regenerative medicine by providing a tool that enables unprecedented flexibility, speed, control, and precision over conventional manufacturing methods. As a result, there has been a growing body of research focused on the development of complex biomimetic tissues and organs produced via 3D printing to serve in various applications ranging from models for drug development to translational research and biological studies. With the eventual goal to produce functional tissues, an important feature in 3D printing is the ability to tune and modulate the microenvironment to better mimic in vivo conditions to improve tissue maturation and performance. This paper reviews various strategies and techniques employed in 3D printing from the perspective of achieving control over physical, chemical, and biological properties to provide a conducive microenvironment for the development of physiologically relevant tissues. We will also highlight the current limitations associated with attaining each of these properties in addition to introducing challenges that need to be addressed for advancing future 3D printing approaches.