Human lungs are organs with an intricate hierarchical structure and complex composition; lungs also present heterogeneous mechanical properties that impose dynamic stress on different tissue components during the process of breathing. These physiological characteristics combined create a system that is challenging to model in vitro. Many efforts have been dedicated to develop reliable models that afford a better understanding of the structure of the lung and to study cell dynamics, disease evolution, and drug pharmacodynamics and pharmacokinetics in the lung. This review presents methodologies used to develop lung tissue models, highlighting their advantages and current limitations, focusing on 3D bioprinting as a promising set of technologies that can address current challenges. 3D bioprinting can be used to create 3D structures that are key to bridging the gap between current cell culture methods and living tissues. Thus, 3D bioprinting can produce lung tissue biomimetics that can be used to develop in vitro models and could eventually produce functional tissue for transplantation. Yet, printing functional synthetic tissues that recreate lung structure and function is still beyond the current capabilities of 3D bioprinting technology. Here, the current state of 3D bioprinting is described with a focus on key strategies that can be used to exploit the potential that this technology has to offer. Despite today’s limitations, results show that 3D bioprinting has unexplored potential that may be accessible by optimizing bioink composition and looking at the printing process through a holistic and creative lens.