Research in cell biology greatly relies on cell-based in vitro assays and models that facilitate the investigation and understanding of specific biological events and processes under different conditions. The quality of such experimental models and particularly the level at which they represent cell behavior in the native tissue, is of critical importance for our understanding of cell interactions within tissues and organs. Conventionally, in vitro models are based on experimental manipulation of mammalian cells, grown as monolayers on flat, two-dimensional (2D) substrates. Despite the amazing progress and discoveries achieved with flat biology models, our ability to translate biological insights has been limited, since the 2D environment does not reflect the physiological behavior of cells in real tissues. Advances in 3D cell biology and engineering have led to the development of a new generation of cell culture formats that can better recapitulate the in vivo microenvironment, allowing us to examine cells and their interactions in a more biomimetic context. Modern biomedical research has at its disposal novel technological approaches that promote development of more sophisticated and robust tissue engineering in vitro models, including scaffold- or hydrogel-based formats, organotypic cultures, and organs-on-chips. Even though such systems are necessarily simplified to capture a particular range of physiology, their ability to model specific processes of human biology is greatly valued for their potential to close the gap between conventional animal studies and human (patho-) physiology. Here, we review recent advances in 3D biomimetic cultures, focusing on the technological bricks available to develop more physiologically relevant in vitro models of human tissues. By highlighting applications and examples of several physiological and disease models, we identify the limitations and challenges which the field needs to address in order to more effectively incorporate synthetic biomimetic culture platforms into biomedical research.