3D organ models have gained increasing attention as novel preclinical test systems and alternatives to animal testing. Over the years, many excellent in vitro tissue models have been developed. In parallel, microfluidic organ-on-a-chip tissue cultures have gained increasing interest for their ability to house several organ models on a single device and interlink these within a human-like environment. In contrast to these advancements, the development of human disease models is still in its infancy. Although major advances have recently been made, efforts still need to be intensified. Human disease models have proven valuable for their ability to closely mimic disease patterns in vitro, permitting the study of pathophysiological features and new treatment options. Although animal studies remain the gold standard for preclinical testing, they have major drawbacks such as high cost and ongoing controversy over their predictive value for several human conditions. Moreover, there is growing political and social pressure to develop alternatives to animal models, clearly promoting the search for valid, cost-efficient and easy-to-handle systems lacking interspecies-related differences. In this review, we discuss the current state of the art regarding 3D organ as well as the opportunities, limitations and future implications of their use.