Tuberculosis (TB) is a devastating disease to mankind that has killed more people than any other infectious disease. Despite many efforts and successes from the scientific and health communities, the prospect of TB elimination remains distant. On the one hand, sustainable public health programs with affordable and broad implementation of anti-TB measures are needed. On the other hand, achieving TB elimination requires critical advances in three areas: vaccination, diagnosis, and treatment. It is also well accepted that succeeding in advancing these areas requires a deeper knowledge of host-pathogen interactions during infection, and for that, better experimental models are needed. Here, we review the potential and limitations of different experimental approaches used in TB research, focusing on animal and human-based cell culture models. We highlight the most recent advances in developing in vitro 3D models and introduce the potential of lung organoids as a new tool to study Mycobacterium tuberculosis infection.